WWIII
Some have argued that a U.S. invasion of Cuba would not actually spark WWIII, but if we go nuclear from the get-go the Soviets have to react or retaliate.
Oh yeah, it'd be WW3 alright, and the Cubans would do pretty well in the first 36 or so hours and then the following guerrilla fighting. Because there would be lots of Guerilla fighting in the mountains, and that's what they planned for. The First couple of days would be use it or loose it time, and then everybody grabs an AKM and an RPG-7 and goes in the woods. Given the US public's memories of Vietnam, and the reduced military funding during the Carter Administration, followed by Reagan's rapid expansion of the Navy, it's an absolutely terrible time to start a major war.
Depending on how long the tensions last before war actually breaks out, the Cubans might try and bring the troops from Angola and Ethiopia home, possibly with some heavy equipment. Hell, the Soviets might ship them a few MiG-23ML/MLAs to beef up their numbers, and get a better idea of how well it'd perform against the current crop of american fighters, which would help with getting an idea of how the Flanker and Fulcrum would do.
Either way, the Cubans would definitely try to launch air raids on NAS Key West at least, and seriously attempt to hit Homestead AFB and SOUTHCOM, maybe aiming for MacDill AFB, the Port of Tampa, Port of Miami and NS Mayport. If they're using their MiG-23BNs (escorted by MiG-21s) they have a reasonable chance of success at hitting NAS Key West and Homestead AFB if they can avoid any 4th Generation fighters on the scene, since the Florida Air National Guard are flying very outdated F-106s.
The Cuban navy might be in the worst shape to fight a war, since they're mostly limited to a few Osa I/IIs and a pair of Foxtrots in offensive terms, but used judiciously, they could do a hell of a lot of dammage too, sinking a few Cruisers and Destroyers.