Step 1
Preheat the oven to 350 degrees F (175 degrees C). Grease and flour three 9-inch round cake pans.
Step 2
Combine sugar and butter in a bowl and cream using an electric mixer until light and fluffy scraping down the sides and blending for a total of 5 minutes. Add egg yolks slowly 1 at a time beating into creamed butter mixture. Beat in vanilla extract.
Step 3
Sift flour baking powder and 1 pinch salt together in a separate bowl. Add to creamed sugar mixture in 3 batches alternating with milk and blending after each addition. Scrape down the sides and bottom of the bowl and blend for 1 minute more; batter should be smooth and consistent. Separate batter evenly into 3 mixing bowls about 2 1/2 cups in each.
Step 4
Beat egg whites and remaining salt together in a bowl using a whip attachment until stiff peaks form.
Step 5
Fold 1/3 of the whipped egg whites into 1 bowl of batter and pour into a prepared cake pan for the vanilla layer.
Step 6
Fold 1/3 of the whipped egg whites and chocolate-flavored milk powder into another bowl of batter. Pour into another prepared cake pan for the chocolate layer.
Step 7
Fold remaining 1/3 of the whipped egg whites strawberry-flavored milk powder and red food coloring into remaining bowl of batter. Pour into the remaining prepared cake pan for the strawberry layer.
Step 8
Bake cake layers in the preheated oven until a toothpick inserted into the center of each comes out clean 25 to 30 minutes. Remove from the oven and cool for about 15 minutes before flipping layers onto a wire rack to cool to room temperature 20 to 30 minutes more.
Step 9
Combine cream cheese butter and shortening in a bowl and cream together until smooth. Scrape down the bowl and add confectioners' sugar. Blend until frosting is smooth.
Step 9
Assemble and frost the cooled cake layers and decorate as you please.