@Sierra02 - I have been on the same quest after my daughter gave me one when she came back from her honeymoon in the Bahamas. I could only find the large Tortuga rum cakes online that sell around thirty dollars a piece, but like you, I wanted to make my own.
The closest thing I could find is to make a simple pound cake using two cups of cake flour, one and a half cup of sugar, four teaspoons of baking powder, one teaspoon of salt, one half cup of butter and three tablespoons of vegetable oil.
After you mix together all of those ingredients then you add a package of vanilla pudding mix, a half cup of milk, four eggs, a half cup of vegetable oil, one teaspoon of vanilla and a half cup of rum.
Pour in a greased Bundt pan and bake for fifty-five minutes at three hundred twenty five degrees or until golden brown.
For the glaze you need to boil a half cup of butter, one fourth cup of water and one cup of sugar. Reduce the heat to a simmer until the sugar is completely dissolved then remove the mixture from the heat and add one half cup of rum.
Add the syrupy glaze to the cake while it's still cooling in the pan, you may have to add it slowly and repeat it several times to fully soak through.