Preheat oven to 350°F.
Prepare one cake mix according to the manufacturer’s instructions. Divide batter evenly into 5 bowls and color each bowl with a different food coloring. Spray a 20-well cake pop mold with non-stick spray and place on a sheet pan. Fill 4 holes with each color of batter, place replace the top on the mold and bake for 16-18 minutes, or until a toothpick inserted into the center comes out clean. Let cool, remove cake balls and use a serrated knife to trim off any excess cake from the spheres.
Butter and line three 6-inch round cake pans with parchment paper. Fill each pan with 6-7 cake balls in an assortment of colors.
Prepare remaining 2 boxes of cake mix according to the manufacturer’s instructions. Pour 3 cups of batter into each cake pan, smooth tops and bake 25-30 minutes or until a toothpick inserted into the center of the white batter (not a cake ball) comes out clean. Let cool completely and invert onto a cutting board. Use a serrated knife to level tops of cakes.
To make lemon buttercream frosting, place butter in the bowl of a stand mixer fitted with a paddle attachment. Mix on medium speed to soften, about 30 seconds. Add all of the sifted powdered sugar, lemon zest and salt, attach splash guard, and mix on low speed until it just comes together, about 3 minutes. Mixture will look very powdery at first. Scrape down sides and bottom of bowl, and mix again to incorporate any loose powdered sugar.
Turn mixer on high and immediately add vanilla extract and lemon juice; mix until just combined, about 20 seconds. Pull off 1 cup of this stiff lemon buttercream for piping decorations. Beat in heavy cream, a teaspoon at a time, to reach a softer, spreadable consistency.
To assemble cake, place the first cake layer on a flat surface and spread with a ½ cup of buttercream frosting. Stack the next cake layer on top, making sure it’s centered and level. Repeat with another layer of buttercream and top with the final cake layer.
Smooth any buttercream that squished out of the edges of the cake and then refrigerate the cake for about 30 minutes, or until the cake tower feels firm enough to frost.
Spread a thin layer on the top and outside for a crumb coat. Refrigerate the cake for at least 30 minutes, until the crumb coat is chilled and no longer feels sticky. Cover the cake in a final layer of buttercream and smooth the top and sides. Decorate the top with piped rosettes and fresh berries.