To make the cake base: Preheat the oven to 350 degrees F.

Grease a 9 by 9-inch cake pan.

Combine all ingredients in a mixing bowl and scrape into the prepared pan. Bake until a cake tester or a toothpick inserted into the center comes out clean, about 30 minutes. Place on a rack to cool for 15 minutes. Turn the cake out of the pan and let cool completely.

To make the towers: Generously grease the cans with shortening. Combine all ingredients in a mixing bowl. Divide the batter among the cans, filling them not more than halfway. Bake until a cake tester, wooden skewer or raw piece of spaghetti inserted into the center comes out clean, about 50 minutes for the smaller cans and 1 1/4 hours for the large can. Place on a rack to cool for 15 minutes. Turn the cakes out of the cans and let cool completely.

To prepare the frosting: Put 2 tubs of frosting in a mixing bowl and add blue food coloring until it reaches the desired shade. Set aside. Divide the remaining tub of frosting between 2 bowls and color 1 purple and 1 pink. Set aside.

To assemble the cake: Place the square cake on a platter and cover with blue frosting. Use a serrated knife to trim the tower cakes so the tops are flat. Cover the towers with blue frosting. Set the large tower on the center of the base cake and then set 1 of the smaller towers on top of it, securing with 1 or 2 straws or skewers. Set 1 small tower on each side of the large one, securing them to the base cake with a straw or skewer (cut to fit as needed).

Cover the sugar cones with purple icing and place open-side down on top of each tower. Use a spatula to smooth out the frosting on the cakes or cones.

Fill the pastry bag with pink icing and pipe a border around the edges of the cake. Insert lollipops around the edge of the base cake to make a fence. Set the doll in front of the main tower and scatter the sprinkles over all.