Allegedly JFK, during the Cuban missile crisis, asked the Joint Chiefs of Staff "What do we do now? Should we nuke Berlin?"

I find that hard to believe. Kennedy was hardly an idiot, and he had witnessed the building of the Berlin wall only a year or so before the Cuban missile crisis. In addition, by many accounts, he was nervous that Khrushchev would provoke an attack in Berlin, so it seems unlikely that he would try to insigate one himself.

You should check out the article Learning from the Missile Crisis, by Max Frankel. Mr. Frankel was one of the few journalists allowed around during the Cuban missile crisis before the situation was made publically known, and he does a good job deconstructing the events surrounding the crisis, including placing some blame on the Kennedy administration for not understanding the Soviet Union well enough, amongst other things. It's very interesting, and says a lot of things that I don't think are well known about the crisis, including looking at it from both the Soviet and Cuban points of view.