Place the remaining ingredients in a large mixer bowl and blend on low speed. Then beat for 4 minutes at medium speed.
Pour the batter into the tube pan and bake for 1 hour, until the cake begins to pull away from the pan. Do not underbake.
Cool the cake for 10 minutes in the pan. Then invert it onto a serving plate and poke holes into the top of the cake with a long wooden skewer. Glaze while the cake is still warm.
Mix butter, sugar, and water in a saucepan over medium-high heat and stir until the mixture comes to a boil. Boil for 5 minutes, stirring constantly. Then stir in the rum and return to a boil. Keep warm.
Spoon and brush the warm glaze evenly over the warm cake. Allow the cake to absorb the glaze, and repeat until all the glaze is used up.