Preheat the oven to 325°F. Spray a 10-inch bundt pan with nonstick cooking spray.
Sprinkle nuts over bottom of pan.
In a large mixing bowl add pudding mixture, flour, sugar, baking powder, and salt. Set aside.
Into the bowl of a stand mixer with the paddle attachment, add the butter. Mix on medium speed for 1-2 minutes.
Add the dry ingredients to the butter and combine for 30 seconds.
Add milk, oil, vanilla, and the eggs, one at a time, and mix on medium-high for one minute, scraping down the sides of the bowl as needed.
Stir in the rum and mix until combined.
Pour batter over nuts and spread batter in an even layer.
Bake 55-60 minutes, or until a toothpick inserted in the center comes out clean.
Remove the cake from the oven and let it cool for about 10 minutes.
After about ten minutes, invert the cake onto a serving plate.