Preheat oven to 325°F and grease and flour a 10-inch Bundt pan. Add the chopped pecans evenly to the bottom of the pan.
Sift the cake mix and pudding mix into a large bowl or stand mixer fitted with a whisk attachment. Beat in the eggs, water, oil, and rums until fully incorporated. Pour the batter over the pecans.
Bake for 1 hour or until a cake tester inserted into the cake comes out clean.
During the last 10 minutes that the cake is baking, prepare the glaze. In a saucepan, combine the butter, water, and sugar and bring to a boil over medium heat. Continue to boil for 5 minutes, stirring constantly. Remove from heat and stir in the rums.
Use a skewer to poke holes all over the cake while in the pan, then pour the glaze all over the cake while both are still hot. Be careful not to let it overflow the pan.
Let the cake cool and soak for at least 2 hours before removing from the pan. DO NOT refrigerate. After the cake has cooled, use a small rubber spatula to loosen it from the sides of the pan, then gently flip it onto a serving dish and remove it from the pan. Be patient and let gravity do it's thing, the cake is a little sticky and is slow to come out.
Once plated, leave plain, dust with powdered sugar, or top with icing and toasted pecan pieces if desired.