Using a large bowl or stand mixer, combine the butter and sugar until creamy. Add in the eggs with the orange zest. Let mix for about one minute.
Add in the flour, baking powder, rum, and milk, mixing until the batter is smooth and creamy.
Pour batter into lightly sprayed bundt cake pan.
Bake for about 25-30 minutes, or until you can stick a toothpick in the center of the cake and it comes out clean.
Set the cake aside to cool. Once cool, flip the cake over on a plate and remove from pan.
Combine the powdered sugar, vanilla, and rum, to the melted butter. Whisk together until smooth and creamy. Pour over rum cake, letting it drizzle down the sides.