Cancun-Havana-Miami? how can I do it?

I am in Cancun, Mexico. I wish to go one-way to Havana, Cuba. From there, I'd like to enter the United States. I have a Canadian passport. My prefered point of entry is Miami. From there, I will work my way to New York, and exit the country from there (to Europe).

My question is can this be done? If it is too much of a problem finding a flight out of Havana (direct to Miami), I will simply skip Cuba and head to the U.S direct from Cancun. I need insight from a traveller who has done this route.

Cancun-Havan-Miami. What I don't want to do is go Cancun-Havana-Cancun-Miami.

Mostly, because I don't have lot of funds.