USSR's involvement in Cuba overshadows their entanglements with other nations in Latin and South America and I would like to know more.
Since no one else has jumped in I'll take a crack at it.
That's a pretty broad question, given the general disparity between nations, but pretty much everything south of El Paso was part of the Non-Aligned Movement during the Cold War (the so-called "third world.") Even within Cuba there was a split as some of the more ideological members saw that the Soviet Union was more interested in using Cuba as a front-line antagonist rather than supporting communism.
Before the rise of the juntas, most of the South and Central American countries pursued anything from moderately left-leaning Import Substitute Industrialization economic policies to outright nationalization of industry, but the cooler heads of state were not eager to trade the Americans for the over-bearing Soviets. Overtures to the Soviets generally came out of necessity.
If you want detailed specifics, and I do mean DETAILED, Christoper Andrew's book on the subject is outstanding. Be prepared for dense reading; I swear this book has it's own gravity, but it's original source material that we would not have if Vasili Mitrokhin hadn't risked his life to get it out of the country. The world was going our way the KGB and the battle for the Third World