Preheat oven to 325 degrees F. Grease and flour a Bundt pan.
Sprinkle nuts in the bottom of the prepared pan. Set aside.
In a large bowl, combine the cake mix, pudding mix, rum, water, vegetable oil and eggs. Beat on medium speed for 2 minutes.
Pour the batter over the nuts in the pan.
Bake for 1 hour, or until a toothpick inserted in the center comes out clean.
About 10 minutes before the cake is done, prepare the glaze. In a saucepan, combine the butter, sugar, rum and water. Boil for 3 minutes, stirring constantly.
Leave the hot cake in the pan and use a toothpick or wooden skewer to poke holes in the bottom of the cake. Slowly drizzle about half of the glaze over the bottom of the cake, allowing time for the glaze to soak into the holes and be absorbed by the hot cake.
Place a wire rack over a foil-lined baking sheet to catch drips. After about 10 minutes in the pan, turn the cake out onto the wire rack (right-side up). Poke holes on the top of the cake. Gradually drizzle remaining glaze over the top of the cake. A lot of the glaze will soak into the cake, and some will also drip down the sides.
Cool completely, then slice and serve!