Preheat the oven to 325 degrees F, grease and flour a bundt pan- See Notes about size
Sprinkle the bottom of the prepared pan with the chopped pecans.
In the mixing bowl, combine the dry ingredients: cake mix, vanilla pudding mix, flour, light brown sugar, cinnamon, baking powder and salt. Whisk to blend.
Then, add the eggs, vegetable oil, mashed bananas, milk, rum, and vanilla extract. With an electric mixer (paddle attachment if using a stand mixer) start mixing the ingredients on low speed until blended (about 15-20 seconds.) Then, increase to medium speed and mix for two minutes. Scrape down the sides and bottom of the bowl as needed. The batter will be runny.
Pour or scoop the batter in the bundt pan and bake for 50-55 minutes or until a wooden skewer/toothpick comes out clean or with just a few crumbs attached. Bake times may vary- check the cake as it approaches the 45 minute mark and adjust time accordingly.
During the last 15 minutes of baking, make the glaze.