Prepare batter according to box directions. Divide batter into three equal portions, into clean bowls, roughly 1 2/3 cup per each. Tint one bowl light blue, another light purple and the other stays white. Transfer to prepare pans. Bake for 25 minutes or until centers are set. Cool in pan until cool enough to handle. Transfer to a wire rack to cool completely. Carefully slice off domed tops from cakes.
Prepare frosting for crumb coating. Mix all ingredients together until smooth. Place blue cake on a clean work surface covered with wax paper strips or a cake board, if desired. Add a thin coat of frosting to the blue cake, top off with purple cake. Repeat frosting layer and top off with white cake. Carefully coat entire top and sides of cake with a thin layer of frosting, sealing in any crumbs. Transfer to the refrigerator to harden for at least several hours or overnight.
Prepare larger frosting batch. Cream together shortening and butter, followed by 1 cup of powdered sugar at a time. Finally, add water and continue mixing until frosting is smooth. Divide into three equal portions, transferring to three clean bowls. Cover white frosting immediately with plastic wrap. Tint a second bowl light blue, to match the cake. Cover well with plastic wrap and repeat process with remaining frosting, tinting purple to match the second cake layer.
Remove cake from refrigerator. Starting from the bottom of the cake, using a small offset spatula, spread a small amount of blue frosting along the bottom tier. It doesn't have to be perfect. Clean spatula. Add purple to the center of the sides of the cake. Clean spatula again, add white to the top and top portion of the sides. Clean and warm spatula as needed to smooth sides and top.
Carefully transfer cake to desired serving plate or cake stand. Touch up edges as needed. Top off with sprinkles.
Store in an airtight container for up to several days.