Preheat oven to 325 degrees F. Grease and flour a 10 inch Bundt pan.
In a medium bowl, put cake mix and pudding mix, eggs, water, oil, coconut flavoring and 1/2 cup coconut rum. Whisk together briskly until well thoroughly mixed.
Bake in the preheated oven for 45 - 50 minutes. The cake is done when a cake tester comes back clean.
Let sit for 15 minutes in the pan. While the cake is resting, make the glaze.
In a medium saucepan, combine butter, water, and brown sugar. Bring to a boil over medium heat and continue to boil for five minutes, stirring constantly.
Remove the glaze from the stove and stir in the rum. Set aside.
Gently slide a rubber spatula between the cake and the Bundt pan to ensure that it is loosened and will release easily.
Carefully invert the cake onto a plate and pour 1/3 of the glaze into the Bundt pan. Slide the cake back off of the plate into the Bunt pan making sure to line up the pattern of the cake and pan correctly.
Pour the rest of the glaze over the cake and allow to sit for one hour and absorb the glaze. Gently invert the wet cake back onto a plate and allow to sit for another hour or until the next day before serving.
Serve with homemade whipped cream or vanilla ice cream.