Preheat the oven to 325 degrees F. Prepare three 8-inch or four 6-inch round cake pans with non-stick spray, parchment paper on the bottom of the pan, and another coat of spray. Set aside.
In a medium size bowl, whisk together the cake flour, baking powder and salt. Set aside.
In the bowl of a stand mixer, fitted with the paddle attachment, beat the butter, oil, sugar and pudding mix on high until fluffy and smooth, about 5 minutes.
Add the eggs and the egg whites, one at a time to the bowl and beat on medium until well incorporated. Add the sour cream and beat on medium speed for a minute or so. It may look curdled, don't stress.
Turn the mixer on low and add 1/3 of the flour mixture to the butter mixture and mix until fully incorporated. Then add half of the buttermilk and blend well, followed by another 1/3 of the flour mixture, the second half of the buttermilk and lastly, add the remaining flour mixture and mix until incorporated.
Add the vanilla extract and beat on low until incorporated. Scrape down the sides of the bowl and mix on low for another 30 seconds.
Evenly distribute the cake batter among the three 8-inch or four 6-inch pans and bake for 23 to 28 minutes, until toothpick comes out with just a few moist crumbs on it.
Remove cakes from the oven and let cool in pans for 10 minutes before inverting onto cooling racks.
When cakes are completely cooled, I like to wrap each cake layer individually with plastic wrap and stick it in the refrigerator or freezer until I’m ready to frost. The cake will be easier to work with if it’s cooled a bit. If I’m making the cake a day or two before I actually need to frost it, I put it in the freezer to ensure freshness. If I’m frosting same-day, I’ll just put it in the refrigerator to chill until needed.