Actually, there was a bit of "love lost" in that Cuba at one time was "wooed" by the United States to become another American territory. Instead, Cuba struck up alliance with America's number one rival, Russia, and the romance was definitely over!
In the 50s (the "hottest" moment of the "Cold War") the incident of Bay of Pigs heightened tension between the two countries, as the United States feared a missle attack from Havanna. A sugar embargo and then rupture of all trade relations ensued.
Below is a personal site as well as an official one listing various documents which you may find of interest.
Cuba's relationship with the US has been and continues to be strained, at best. Between the US trade embargoes, our divergent political systems, and the historically beligerent position of past dictators in relation to the US, Cuba continues to be in a near-adversarial position to the US. There is no love lost between the countries, and looking all the way back to the 1960s, ever since the Cuban Missile Crisis took place, relations between the two countries have remained stale.