Heat oven to 350 degrees F. Butter and flour an 9 by 2-inch round pan and a 9 by 9 by 2-inch square pan. Combine the sugar and marzipan in a food processor. Pulse until combined into fine crumbs. Cream the butter in a mixer fitted with a paddle attachment (or using a hand mixer) until smooth. Add the sugar-marzipan mixture and mix. Add the vanilla and mix. Add the eggs two at a time, mixing after each one. Sift the flour, baking powder, salt, and ginger together. Working in batches, add the dry ingredients to the marzipan mixture, mixing after each addition just until combined. Bake for 40 to 45 minutes, until a tester inserted into the center comes out dry and clean (a few crumbs are okay) and let cool in the pan.
Combine sugar and water and bring to a boil on a medium saucepan. Boil until a candy thermometer registers 240 degrees F. Whip egg yolks until light and fluffy and carefully pour the sugar water mixture into the yolks while the mixer is running at a moderate speed. Continue whipping until cooled. Add softened butter in small batches, stopping after each addition. Remove the 9-inch round cake from the pan, and cut a 5-inch and a 3-inch circle of cake from the 9-inch square pan. Cover them with butter cream and freeze. Dye fondant pastel pink, blue and yellow by kneading food coloring into it. Roll out on a powdered sugared surface and cut 1 circle out of each color to cover 1 layer of the cake, leaving 2 extra inches to hang over sides. Lay the fondant over the cake layers and with your hands, mold the fondant over the cake to fit. Trim the edge and tuck it slightly under the cake. On a large cake platter, stack the layers and run a long skewer down the center.
Whip together powdered sugar and 3 to 4 tablespoons of the egg whites so it's pipe-able but not too thin that it runs on the cake. Decorate cake with piped royal icing using a plain small tip, starting at the bottom layer. You can embellish with silver balls, gum paste flowers on top, etc.
Consumption of raw or undercooked eggs, shellfish and meat may increase the risk of foodborne illness.