Preheat your oven to 350 degrees and prepare three 8- inch cake pans by rubbing generously with vegetable shortening and dust with flour and set aside.
In a medium bowl, add the flour, instant pudding mix, baking powder, and salt. Whisk and set aside.
In the bowl of a stand mixer equipped with a paddle attachment, cream the butter, brown sugar, and granulated sugar until fluffy.
Add the vegetable oil, vanilla, and rum extract. Mix until just combined.
Add the eggs, one at a time, and combine after each addition.
Add half of the dry ingredients and mix until there are no dry spots remaining.
Slowly pour in the milk and mix until fully combined.
Add the remaining dry ingredients and mix until there are no dry spots remaining. Scrape the sides and bottom of the bowl to insure all the ingredients were mixed well.
Divide the batter evenly between the three prepared pans and gently tap on the counter to remove any air bubbles.
Bake for 22-25 minutes or until a toothpick inserted in the center of the cake comes out clean.
Remove form the oven and allow to cool in the pans for 10 minutes then invert onto a wire rack to cool completely.