Spray 3 (9-inch) cake pans with nonstick spray, then coat lightly with flour.
Prepare cake mix according to package directions; stir in sprinkles.
Divide batter evenly between cake pans. Bake until a toothpick inserted in the center comes out clean, about 10 to 12 minutes.
Let cake cool slightly, then remove cake from pans and transfer to a wire rack to cool completely before frosting.
Use a 2.5-inch circle cutter to cut each layer into 7 circles. (Tip: If your cake layers have a dome after baking, slice off the tops with a serrated knife before cutting out the circles.)
Cover a cake circle generously with frosting. Add another cake layer and frost, then add 1 more layer. Frost top of cake.
Use the flat side of a knife to remove excess frosting from the sides of the cake. Top cake with sprinkles.