This is an old term, dating back to the mid 1800´s. It became a modern cocktail around 1902, when American soldiers and businesses flooded into Cuba at Spain’s capitulation after the Spanish-American war.
One of these companies was the then very new Coca-Cola, which began sending its cola syrup to Cuba beginning in 1902.
By that time, Americans were already trained cocktail drinkers and very talented at mixing highballs of all kinds. Coca-Cola enhanced with a dose of spirits was becoming very popular, and thus the „Cuba Libre“ was born. Very important is the lime! Lime is the difference between Cuba Libre and Rum and Coke.