Preheat the oven to 325°F. Grease and flour a Bundt pan with at least a 10-cup capacity. Sprinkle the pecans in the bottom of the pan.
With a mixer, mix together the cake mix, pudding mix, eggs, vegetable oil, water, and rum. Continue mixing until well combined. Pour the batter over the pecans.
Bake for 50 to 60 minutes, or until a toothpick inserted into the middle part of the cake comes out clean and the cake starts to pull away from the edges of the pan.
Make the glaze by combining the butter, sugar, and water in a small saucepan. Bring to a boil then remove from the heat. Stir in the rum.
Poke holes all over the top of the cake with a skewer or toothpick. Pour the glaze over the warm cake while it is still in the pan. Once the glaze has all soaked in and the cake in just barely warm, invert it out onto a serving platter. brush any remaining glaze over the cake. If your cake sticks, don't force it out. Simply place it in a 350° oven for about 10 minutes to warm the sugars stuck to the pan, then turn it out.
