What were Russia's true intentions in the Cuban Missile Crisis?

They wanted to put pressure on the US by using Cuba as a bargaining chip. Cuba had recently undergone a socialist revolution bringing Castro into power. The US wanted to overthrow Castro's regime while the USSR wanted Castro to remain because he was sympathetic to them and that meant Cuba was part of their 'sphere of influence'.

I don't think Kruschev really wanted to start World War 3, although it understandably looked that way to many people at the time. The fact that he was ready and willing to negogiate with Kennedy bears that out. He was waging a war of nerves, in which the nukes were sabres which were rattled but that was all. We all know the outcome - the USSR agreed to remove their nukes from Cuba and Castro remained in power, his regime having now outlived the Soviet Union.

Edit: qasw, you're right, the US agreed to withdraw their nukes from Turkey in return.

It was to get the US to pull the nuclear missiles out of Turkey. Which they did.

Few people know that the Cuban Missile crisis was precipitated by the US placing missiles across the border from Russia in Turkey. This was before the Soviets put missiles in Cuba.

The Soviets did not threaten war, but they did retaliate by putting missiles in Cuba.

The Soviets were upping the ante, in a manner of speaking. The missiles could only be a first strike weapon, they would be ineffective as a deterrent; if the U.S. truly wanted to do a first strike they could be easily taken out with bombers. With the advent of the submarine launched ballistic missile, they were unnecessary, submarines could hide, Cuba could not. Khrushchev may have believed that Kennedy would back down, and allow the missiles to stay, based on their meetings in Vienna. He may have believed Kennedy to be weak and easy to manipulate. He could have moved missiles there during the '50's, but was unwilling to test Eisenhower, feeling that Eisenhower, a career soldier, wouldn't be lacking in resolve.

I think Russia said "Hey, the US is building nuclear sites all over OUR back yard (Western Europe) - Why don't we build some in their area to make things fair?"

Russia was allies with Cuba, just as we were allies with West Germany and France.

Maybe it was a test for Kennedy or maybe they just wanted the U.S. missles out of Turkey, which is what they got in the end.

strategic threat nothing more nothing less.

whatever it was it was probably not above board and very devious