For the cake: Grease a Bundt pan and spread pecans on the bottom of the pan. Beat eggs, oil, water and rum in mixer just until incorporated. Add pudding mix and cake mix and beat on med, about 3 to 5 minutes just until you get a smooth texture. Pour into pan and bake at 350 degrees F for 40 to 45 minutes. The cake should have a light golden brown color, but will darken with the glaze.
For the glaze: Melt butter in saucepan and add the sugar and water, bring to a boil. Once it starts to boil, take off the heat and add the rum. Pour into a large measuring cup that will hold that amount or more. Set aside.
Once cake is ready, take out of oven and leave in pan. Gently prick holes into the cake with a skewer. Slowly pour half of the glaze over the cake making sure to fill in all the holes. Once the cake has soaked up the glaze, turn cake over, removing pan, onto the base that the cake will stay on. Gently prick more holes on other side and slowly pour other half of glaze over cake. Fill the center of the cake with reserved pecans. Let cool and enjoy. The cake is best if left at room temperature.
The glaze needs to be prepared approximately 10 minutes before cake is ready. Make sure you have plenty of paper towels underneath the base as the glaze will run down the sides of the cake.