Preheat the oven to 325℉.
In a large mixing bowl of a stand mixer or using a hand beater, beat the eggs and then gradually add the oil, water and rum. Add the cake mix and vanilla pudding. Mix and set aside.
Generously grease a 10" Bundt pan with cooking spray or liquid vegetable shortening (use a pastry brush to make sure you cover every crevice of the pan so the cake releases easily after baking) or vegetable shortening in a stick form using a paper towel or your fingers.
Spread the toasted nuts over the bottom of the Bundt pan.
Stir the cake batter then slowly spoon the batter evenly over the nuts. When finished, tap the bottom of the pan on a work surface to release any bubbles in the batter.
Bake for 50 minutes to one hour or until a toothpick inserted in the cake comes out clean.
When the cake is done, remove it from the oven and set it on a wire rack to cool for 10 minutes (cooling longer in the pan will cause the cake to stick to the pan prior to flipping it).
After 10 minutes, tap the bottom of the pan on a work surface to help loosen the cake, carefully lay your serving plate over the top of the bundt pan then invert the pan. The cake should drop out of the pan. Remove the pan and prick the top and the sides of the cake with a long toothpick, skewer or fork.