In addition to presidential candidates who won the popular vote but lost the election (Al Gore in 2000 and Samuel Tilden in 1876 come to mind), there have been two people for which the statement as written is literally true:
Andrew Jackson won a plurality (not a majority, but more votes than any other candidate) of both the popular and electoral vote in the presidential election of 1824. However, since there were four candidates in the race that year and none of them had a majority, the decision went to the House of Representatives, who chose John Quincy Adams instead. Jackson then went on to later became president in the election of 1828, with a clear majority of both the popular and electoral vote, so for him the statement is true in retrospect, but not at the time of the first election.
Grover Cleveland also won a plurality of the popular vote in 1888 after his first term as president, though in his case he lost the electoral vote to Benjamin Harrison. He then ran again in 1892 and again won a plurality of the popular vote, but this time garnered a clear majority of the electoral vote and became president for a second time. He's the only one for whom the statement was true at the time of the election itself.
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President George H. W. Bush won the election of 1988 then lost the election of 1992, after which he did not run again. His son, President George W. Bush, never lost a Presidential election.
One example of a candidate who fits this description is Richard Nixon. He first ran for president in 1960 against John F. Kennedy and lost, then ran again in 1968 and won the election. Nixon served as the 37th President of the United States from 1969 to 1974.
He won the popular and electoral vote. Actually he didn't win the popular vote and thought he had lost the election. In a nutshell, he became president when he was able to broker a "backroom" deal with the Democrats.
But still lost the election. Your welcome.
The pardon granted to Nixon by Ford probably cost him the election.