This is the way I cycled Cuba in May 2015. It took me 5 weeks, and I had not really planned my route in advance. So we relied upon what we found out along the route, and this was a great decision. I still think that traveling is a form of freedom, and sticking to plans is the opposite of being free.
Let me show you the map with my comments first. I will add some text below a little later.
Cycling the east of Cuba
Cycling the west of Cuba