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.
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Bitcoin's origin story sounds like something out of science fiction: It was launched in 2008 on the heels of a white paper published by the mysterious Satoshi Nakamoto, whose real identity – and country of origin – are unknown. Nakamoto conceived of Bitcoin as a currency that was 1) encrypted; 2) decentralized, i.e. it was ungoverned and did not belong to any nation; and 3) a digital "distributed ledger," such that everyone can verify online the legitimacy of transactions.

If the private key is lost, the bitcoin network will not recognize any other evidence of ownership;[30] the coins are then unusable, and effectively lost. For example, in 2013 one user claimed to have lost 7,500 bitcoins, worth $7.5 million at the time, when he accidentally discarded a hard drive containing his private key.[74] A backup of his key(s) would have prevented this.

Bitcoin (BTC) is a cryptocurrency which is regarded as the world’s first decentralized digital currency. It was created by a pseudonymous person or persons named Satoshi Nakamoto in 2009 and has since gone on to become the world’s most popular cryptocurrency by market cap. Bitcoin is a deflationary currency whose issuance is capped at a total supply of 21 million coins. Each Bitcoin can be divided into one million units, with the smallest unit of 0.00000001 known as a satoshi in homage to its creator. The distributed public ledger that Bitcoin uses to record transactions is known as a blockchain and Bitcoin can be spent at over 100,000 online merchants and can also be held as an investment. Bitcoin is traded for fiat and other cryptocurrencies on various exchanges but can also be used to facilitate p2p transactions. Each transaction incurs a small transaction fee to cover the cost of sending Bitcoin over the blockchain ledger, with the fee going to miners tasked with keeping the network secure.
^ Jump up to: a b c d Joshua A. Kroll; Ian C. Davey; Edward W. Felten (11–12 June 2013). "The Economics of Bitcoin Mining, or Bitcoin in the Presence of Adversaries" (PDF). The Twelfth Workshop on the Economics of Information Security (WEIS 2013). Archived (PDF) from the original on 9 May 2016. Retrieved 26 April 2016. A transaction fee is like a tip or gratuity left for the miner.
Numerous people have been suggested as possible Satoshi Nakamotos by major media outlets. On Oct. 10, 2011, The New Yorker published an article speculating that Nakamoto might be Irish cryptography student Michael Clear, or economic sociologist Vili Lehdonvirta. A day later, Fast Company suggested that Nakamoto could be a group of three people – Neal King, Vladimir Oksman and Charles Bry – who together appear on a patent related to secure communications that was filed two months before was registered. A Vice article published in May 2013 added more suspects to the list, including Gavin Andresen, the Bitcoin project’s lead developer; Jed McCaleb, co-founder of now-defunct Bitcoin exchange Mt. Gox; and famed Japanese mathematician Shinichi Mochizuki. 
But, as always, the miners’ biggest challenge came from bitcoin itself. The mere presence of so much new mining in the Mid-Columbia Basin substantially expanded the network’s total mining power; for a time, Carlson’s mine alone accounted for a quarter of the global bitcoin mining capacity. But this rising calculating power also caused mining difficulty to skyrocket—from January 2013 to January 2014, it increased one thousandfold—which forced miners to expand even faster. And bitcoin’s rising price was now drawing in new miners, especially in China, where power is cheap. By the middle of 2014, Carlson says, he’d quadrupled the number of servers in his mine, yet had seen his once-massive share of the market fall below 1 percent.
Behind the scenes, the Bitcoin network is sharing a massive public ledger called the "block chain". This ledger contains every transaction ever processed which enables a user's computer to verify the validity of each transaction. The authenticity of each transaction is protected by digital signatures corresponding to the sending addresses therefore allowing all users to have full control over sending bitcoins.

Several news outlets have asserted that the popularity of bitcoins hinges on the ability to use them to purchase illegal goods.[128][224] Nobel-prize winning economist Joseph Stiglitz says that bitcoin's anonymity encourages money laundering and other crimes, "If you open up a hole like bitcoin, then all the nefarious activity will go through that hole, and no government can allow that." He's also said that if "you regulate it so you couldn’t engage in money laundering and all these other [crimes], there will be no demand for Bitcoin. By regulating the abuses, you are going to regulate it out of existence. It exists because of the abuses."[225][226]
On 1 August 2017, a hard fork of bitcoin was created, known as Bitcoin Cash.[103] Bitcoin Cash has a larger block size limit and had an identical blockchain at the time of fork. On 24 October 2017 another hard fork, Bitcoin Gold, was created. Bitcoin Gold changes the proof-of-work algorithm used in mining, as the developers felt that mining had become too specialized.[104]
Steve Wright and John Stoll: The Dam Masters Wright, left, and Stoll, pictured at the Rocky Reach Dam, are general manager and head of customer utilities with the Chelan County Public Utility District, respectively. In the past year, miners have made inquiries or requests for power totaling two-thirds as much as the basin’s three county utilities now generate. | Patrick Cavan Brown for Politico Magazine
Claiming to be the "world's most popular digital wallet," boasts more than 24 million wallets and has supported more than 100 million transactions. Security is a top priority, and with many longtime cryptocurrency enthusiasts comfortably keeping their spoils there for years, even as Mt. Gox and Bitfinex were breached, it would have to be.
At this point, the actual mining begins. In essence, each miner now tries to demonstrate to the rest of the network that his or her block of verified payments is the one true block, which will serve as the permanent record of those 2,000 or so transactions. Miners do this by, essentially, trying to be the first to guess their block’s numerical password. It’s analogous to trying to randomly guess someone’s computer password, except on a vastly larger scale. Carlson’s first mining computer, or “rig,” which he ran out of his basement north of Seattle, could make 12 billion “guesses” every second; today’s servers are more than a thousand times faster.
In January 2009, the bitcoin network was created when Nakamoto mined the first block of the chain, known as the genesis block.[18][19] Embedded in the coinbase of this block was the following text: "The Times 03/Jan/2009 Chancellor on brink of second bailout for banks."[10] This note has been interpreted as both a timestamp and a comment on the instability caused by fractional-reserve banking.[20]:18