Why did the Russians pull their nukes of Cuba

The Soviets decided to pull their nuclear weapons of Cuba after reaching an agreement with the United States in October 27, 1962. According to this agreement, President Kennedy agreed to remove missiles from Turkey and Southern Italy, as long as Soviet leader Nikita Khrushchev removed all missiles from Cuba. The agreement was most likely reached due to the fact that the leaders of both countries knew that a war would be costly, difficult and extremely deadly.

response to the failed Bay of Pigs and the presence of American Jupiter ballistic missiles in Italy and Turkey

Explanation:

Unknown to the Americans, the Soviets had brought some 100 tactical nuclear weapons to Cuba - 80 nuclear-armed front cruise missiles (FKRs), 12 nuclear warheads for dual-use Luna short-range rockets, and 6 nuclear bombs for IL-28 bombers.

In response to the failed Bay of Pigs Invasion of 1961 and the presence of American Jupiter ballistic missiles in Italy and Turkey, Soviet leader Nikita Khrushchev agreed to Cuba's request to place nuclear missiles on the island to deter a future invasion