• Preheat oven to 350 degrees. In a standing mixer, stir together flour, sugar, baking powder, and salt. Beat the butter into the flour mixture, one cube at a time. Continue to beat until it resembles coarse crumbs.
• In a small bowl, whisk together eggs, buttermilk, oil, and vanilla. Add the 1/2 of the egg-milk mixture and oil and beat the batter is light and fluffy. Add remaining egg-milk mixture and vanilla pudding and mix just until combined. Take a spatula and scrape the sides of the bowl. Add rainbow sprinkles and fold into batter.
• Spread into greased (with non-stick cooking spray or butter/flour) 8 or 9-inch cake pans and smooth tops with a spatula. Bake for 16-22 minutes, depending on the depth of pans. If the cake layers are thin, they will cook for less time than the thicker layers.
• Let cakes cool. Run a knife around edge of cake pan and flip over. Frost with vanilla frosting.

Vanilla Frosting:

• In a large mixing bowl, cream together butter and softened cream cheese for 2-3 minutes, scraping the sides of the bowl. Add powdered sugar and vanilla and cream together for several minutes. Add cream or milk, if needed. 
• Frost the cake and top with rainbow sprinkles.