How the Cuban Missile Crisis Added to Tension

Cuba's government, lead by Fidel Castro, released thousands of exiles into the United States, causing a massive invasion at Bay of Pigs. Tension between the United States and Cuba was at its peak, forcing the United States to impede the invasion by mass destruction of Cuban ships and weaponry. Although the US and Cuba had their disputes, the Soviet Union saw Cuba as a reasonable ally to begin the development of missile sites.
The alliance formed by the Soviet Union and Cuba created more exasperation between the US and Soviet relationship. It threatened the United States in a different way than before because it could have given Russia an advantage during a possible nuclear war.
Ultimately, since President Kennedy placed a quarantine on the construction of missiles and offensive weapons, Russia didn't have access to an "advantage," but the tension between the US and Soviet Union was still present.