No, the US should lift the embargo.
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The Cold War is over
The Cuban embargo was created in response to the threat of global communism. Tensions reached their peak in the Cuban missile crisis in 1962. The USSR has since collapsed, and the Cuban threat along with it.
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The embargo against Cuba was enacted during the Cold War, in response to the revolution. It was an attempt to protect America from a Communist power on its doorstep. During the Cuban missile Crisis, the Soviet Union tried to place nuclear weapons in Cuba. The Soviet Union has since collapsed, and the threat that Cuba posed as a satellite state has passed. The embargo is a relic of a different time. The last of the Cold War tension died with the disagreeable Fidel Castro. The embargo served its purpose in the 1960s when economic restrictions forced Castro’s revolutionary army to cut its numbers considerably, but in an era when global communism is no longer spreading, it is no longer necessary. The strategic importance of Cuba is no longer relevant. US intelligence agencies have released a series of statements that Cuba is no longer a military threat to the US. This is universally agreed upon internationally. The United Nations has supported a repeal of the embargo since the early 90s when the Soviet Union collapsed. The sanctions against Cuba made strategic sense during the Cold War but are no longer relevant.
The embargo is not only about the Cold War. Cuba is one of the US’s closest neighbors and as a result has taken most of the refugees fleeing Cuba’s oppressive regime. This has made the Cuban-American lobby a big voice in politics, as many Cuban immigrants care deeply about what happens in their country of origin and to their families. Cuba has remained hostile to America since the end of the Cold War. In 1996, Cuba shot down two civilian US planes.  More recently, Cuba has jailed an American aid worker, sold arms to North Korea, and made deals with Venezuela.  Cuba’s hostility towards the US has not been ended by the cold war. Cuba is of continuing importance to the Cuban-Americans, many of whom fled the Castro regime.
[P1] The sanctions were put in place because of the Cold War which is now over. [P2] Cuba is no longer a threat to the US. [C] The embargo is an anachronism and should be repealed.
Rejecting the premises
[Rejecting P2] Cuba remains hostile to the US