It depends when it occurs, 1949 as in OTL, earlier or later but I doubt wouldn't use it without a direct war against the west. They would use it instead to extract concessions such as with Turkey, Iran and Korea, the notes on a neutral Germany may be given more discussion as well. If the Cuban revolutionary war still succeeds and the US still dismisses them, it's like that the Cuban missile crisis comes out as a clear Soviet victory.
The reaction in the west will be the panic caused by Sputnik x 100 for the public, their representatives and the military. Ridiculous amounts of money will be thrown into an American bomb project, much higher than OTL's Manhattan Project with scientists being forced to cut every corner to deliver a bomb as quickly as possible.
We also need to look at the possible butterflies of this though, without the Atomic bombing of Japan it's probable Stalin would have unified Korea and taken Hokkaido, possibly even a part of northern Honshu. This may set things up for a Japanese civil war instead of Korea.