Yes it can—but it won’t do it much good. The reason is that Google’s servers aren’t fit for solving the Bitcoin mining problem in the same way that ASICs are. For reference, if Google harnesses all of its servers for the sole purpose of mining Bitcoin (and abandons all other business operations), it will account for a very small percent (less than 0.001%) of the total mining power the Bitcoin network currently has.
Skipping over the technical details, finding a block most closely resembles a type of network lottery. For each attempt to try and find a new block, which is basically a random guess for a lucky number, a miner has to spend a tiny amount of energy. Most of the attempts fail and a miner will have wasted that energy. Only once about every ten minutes will a miner somewhere succeed and thus add a new block to the blockchain.
That constraint is what makes the problem more or less difficult. More leading zeroes means fewer possible solutions, and more time required to solve the problem. Every 2,016 blocks (roughly two weeks), that difficulty is reset. If it took miners less than 10 minutes on average to solve those 2,016 blocks, then the difficulty is automatically increased. If it took longer, then the difficulty is decreased.
Armory is the most mature, secure and full featured Bitcoin wallet but it can be technologically intimidating for users. Whether you are an individual storing $1,000 or institution storing $1,000,000,000 this is the most secure option available. Users are in complete control all Bitcoin private keys and can setup a secure offline-signing process in Armory.

Although it is possible to handle bitcoins individually, it would be unwieldy to require a separate transaction for every bitcoin in a transaction. Transactions are therefore allowed to contain multiple inputs and outputs, allowing bitcoins to be split and combined. Common transactions will have either a single input from a larger previous transaction or multiple inputs combining smaller amounts, and one or two outputs: one for the payment, and one returning the change, if any, to the sender. Any difference between the total input and output amounts of a transaction goes to miners as a transaction fee.[2]

Technically, during mining, the Bitcoin mining software runs two rounds of SHA256 cryptographic hashing function on the block header. The mining software uses different numbers called the nonce as the random element of the block header for each new hash that is tried. Depending on the nonce and what else is in the block the hashing function will yield a hash of a 64-bit hexadecimal number.  To create a valid block, the mining software has to find a hash that is below the difficulty target.

Let your computer earn you money with Bitcoin Miner, the free easy-to-use Bitcoin miner! Earn Bitcoin which can be exchanged for real-world currency! Works great at home, work, or on the go. Download Bitcoin Miner and start mining Bitcoin today! Bitcoin miners perform complex calculations known as hashes. Each hash has a chance of yielding bitcoins. The more hashes performed, the more chances of earning bitcoins. Most people join a mining pool to increase their chances of earning bitcoins. Mining pools pay for high value hashes known as shares. The default mining pool issues payouts weekly to accounts with at least 5000 Satoshis. If an account doesn't reach 5000 Satoshis during a week, the balance carries forward (it is never lost).
As noted in Nakamoto's whitepaper, it is possible to verify bitcoin payments without running a full network node (simplified payment verification, SPV). A user only needs a copy of the block headers of the longest chain, which are available by querying network nodes until it is apparent that the longest chain has been obtained. Then, get the Merkle branch linking the transaction to its block. Linking the transaction to a place in the chain demonstrates that a network node has accepted it, and blocks added after it further establish the confirmation.[2]
A mining pool sets a difficulty level between 1 and the currency’s difficulty. If a miner returns a block which scores a difficulty level between the pool’s difficulty level and the currency’s difficulty level, the block is recorded as a ‘share’. There is no use whatsoever for these share blocks, but they are recorded as proof of work to show that miners are trying to solve blocks. They also indicate how much processing power they are contributing to the pool the better the hardware, the more shares are generated.

Bitcoin (BTC) is down a little under percent on the day, and is trading at $6,470 as of press time. With one notable exception Oct. 15 – a brief spike correlated with Tether’s slight untethering from its dollar peg – the top coin has been trading sideways between $6,500-$6,500 for the past few days, before slipping below the $6,500 today, still above where it started the week, close to $6,300. On the week, Bitcoin is 2.7 percent in the green, and is also up just about 2 percent on the month.
You’ll need a Bitcoin wallet in which to keep your mined Bitcoins. Once you have a wallet, make sure to get your wallet address. It will be a long sequence of letters and numbers. Each wallet has a different way to get the public Bitcoin address, but most wallets are pretty straightforward about it. Notice that you’ll need your PUBLIC Bitcoin address and not your private key (which is like the secret password for your wallet).
According to the European Central Bank, the decentralization of money offered by bitcoin has its theoretical roots in the Austrian school of economics, especially with Friedrich von Hayek in his book Denationalisation of Money: The Argument Refined,[120] in which he advocates a complete free market in the production, distribution and management of money to end the monopoly of central banks.[121]:22
Various journalists,[204][211] economists,[212][213] and the central bank of Estonia[214] have voiced concerns that bitcoin is a Ponzi scheme. In 2013, Eric Posner, a law professor at the University of Chicago, stated that "a real Ponzi scheme takes fraud; bitcoin, by contrast, seems more like a collective delusion."[215] A 2014 report by the World Bank concluded that bitcoin was not a deliberate Ponzi scheme.[216]:7 The Swiss Federal Council[217]:21 examined the concerns that bitcoin might be a pyramid scheme; it concluded that, "Since in the case of bitcoin the typical promises of profits are lacking, it cannot be assumed that bitcoin is a pyramid scheme." In July 2017, billionaire Howard Marks referred to bitcoin as a pyramid scheme.[218]

Market Risk: Like with any investment, Bitcoin values can fluctuate. Indeed, the value of the currency has seen wild swings in price over its short existence. Subject to high volume buying and selling on exchanges, it has a high sensitivity to “news." According to the CFPB, the price of bitcoins fell by 61% in a single day in 2013, while the one-day price drop in 2014 has been as big as 80%.
A few years ago, CPU and GPU mining became completely obsolete when FPGAs came around. An FPGA is a Field Programmable Gate Array, which can produce computational power similar to most GPUs, while being far more energy‐efficient than graphics cards. Due to its mining efficiency, and ability to consume relatively lesser energy, many miners shifted to the use of FPGAs.

You’ll need a Bitcoin wallet in which to keep your mined Bitcoins. Once you have a wallet, make sure to get your wallet address. It will be a long sequence of letters and numbers. Each wallet has a different way to get the public Bitcoin address, but most wallets are pretty straightforward about it. Notice that you’ll need your PUBLIC Bitcoin address and not your private key (which is like the secret password for your wallet).

All mining ASICs, Bitmain’s included, are performing essentially the same computation—the SHA-256 hashing algorithm—even if they go about it a bit differently. The standard algorithm takes 64 steps to complete, but in Bitcoin it is run twice for each block header, meaning a full round requires 128 steps that are heavy on integer addition. “That’s what dominates the whole design,” says Timo Hanke, the chief cryptographer at String Labs, a cryptography-focused incubator in Palo Alto, Calif. “So, if somebody was to optimize it, they have to optimize the adders. That’s where most of the work is.”
To be accepted by the rest of the network, a new block must contain a so-called proof-of-work (PoW).[64] The system used is based on Adam Back's 1997 anti-spam scheme, Hashcash.[5][79] The PoW requires miners to find a number called a nonce, such that when the block content is hashed along with the nonce, the result is numerically smaller than the network's difficulty target.[3]:ch. 8 This proof is easy for any node in the network to verify, but extremely time-consuming to generate, as for a secure cryptographic hash, miners must try many different nonce values (usually the sequence of tested values is the ascending natural numbers: 0, 1, 2, 3, ...[3]:ch. 8) before meeting the difficulty target.