Preheat oven to 325°F (165°C). Grease and flour a bundt pan.
In a large bowl, cream together the butter and sugar until light and fluffy.
Beat in the eggs one at a time, then stir in the vanilla.
Combine the flour, baking powder, and salt; stir into the batter alternately with the milk. Mix in the rum.
Pour batter into the prepared bundt pan.
Bake for 60 minutes, or until a toothpick inserted into the cake comes out clean.
To make the glaze: In a saucepan, combine butter, water, and sugar. Bring to a boil and continue boiling for 5 minutes, stirring constantly. Remove from heat and stir in the rum.
Prick the top of the cake and drizzle the glaze over the cake while it is still in the pan. Let the cake absorb the glaze and cool completely before removing from the pan.