Originally Posted by LCSinTexas

Cuba is a unique situation. You cannot fly there from the US, regardless of which passport you use, unless you travel for very specific reasons. I believe it is mostly "for education or for investment" purposes. Check the US site travel.state.gov for more info.
Try going to Cuba by way of Canada or Mexico as they have much lighter regulations.
I am honestly not sure if it can be done as part of a RTW.
Otherwise make a stop in either Mexico or Canada, and do a separate round-trip to to Cuba on another ticket.