Preheat oven to 325°F (165°C). Grease and flour a bundt pan.
Cream butter and sugar until light and fluffy. Add eggs one at a time, beating well after each addition.
In another bowl, combine flour, baking powder, and salt. Gradually add to the butter mixture, alternating with milk. Stir in rum and vanilla.
Pour batter into prepared pan. Bake for 60 minutes or until a toothpick inserted into the center comes out clean.
For the glaze, combine butter, sugar, and water in a saucepan. Bring to a boil and cook for 5 minutes, stirring constantly. Remove from heat and stir in rum.
While the cake is still warm, poke holes all over it with a skewer. Pour the glaze over the cake, allowing it to soak in. Let the cake cool completely before serving.
Notes:
This rum cake is best made a day ahead to allow the flavors to meld.