Preheat your oven to 325°F (165°C). Grease and flour a bundt pan.
In a large mixing bowl, cream the butter and sugar until light and fluffy.
Add the eggs one at a time, beating well after each addition.
In another bowl, combine the flour, baking powder, and salt. Gradually add to the creamed mixture alternately with milk, beginning and ending with the flour mixture. Beat well after each addition.
Stir in the rum and vanilla extract.
Pour the batter into the prepared bundt pan. Bake for 60 minutes or until a toothpick inserted into the center comes out clean.
While the cake is baking, prepare the rum glaze. In a saucepan, combine butter, sugar, and water. Bring to a boil and cook for 5 minutes, stirring constantly. Remove from heat and stir in the rum.
When the cake is done, remove it from the oven and let it cool in the pan for 10 minutes. Invert the cake onto a serving plate. While the cake is still warm, brush the glaze over the top and sides. Allow the cake to absorb the glaze and repeat until all the glaze is used.