In spite of its name, Mount Gay Sugar Cane Rum/Brandy is made from molasses and not sugar cane juice. As far as I know, all rum made in Barbados is molasses based. Indeed it's very difficult to find any "Rhum Agricole" in any of the anglophone Caribbean countries.
Incidentally, I've just started a bottle of Mount Gay Sugar Cane Brandy which I bought in Antigua a couple of weeks ago. Unlike other Mount Gay products, the Sugar Cane Brandy is unavailable here in London - I've always assumed that this is because European Union regulations insist that any product labelled "Brandy" has to be real brandy and not rum. Is this correct, or is there some other reason?