So easy to make.
One box of cake mix makes two round. Six layers = three boxes. Each box, make and divide in half. You'll end up with six bowls of mix. Dye each one. Dye goes a long way. Red, less so. In fact they sell "No taste red" because you'll need so much. You'll spend so much time in pink and salmon. Bake all six, two at a time.
Frosting is stupidly easy to make but a little time consuming. I see they used white between the layers. The outside too, but dyed. Don't do that. Dying white frosting black takes a lot of dye, and white frosting on white cake? Eh, no.
White frosting is easy. Beat a stick of butter and half a stick of shortening. And vanilla extract, about a teaspoon, or two. Fold in sifted powdered/confectioner's sugar, a cup at a time. Four cups total. Blend thoroughly after each cup. Comes out chalky in texture. Add a splash of milk to make it creamier. You can use various extracts in place of vanilla if you want to give it flavor.
Chocolate frosting is just as easy. Stick of butter, half a stick of shortening, 3/4 cup baking chocolate (powder), and 3 cups of the sifted powdered sugar, added a cup at a time. This gets thick, fast. Add a splash of milk after the last couple cups, you'll need it. More milk = more spreadable.
Cakes. Let them sit for ~1-1.5 hours. Stick them in the freezer. Using a big knife, or a cake leveler if you have one, cut the domes off them so they are even. Set aside the trimmings, snack on or offer as snacks. For your now flat six cakes, turn the purple one over, bottom up. Frost. Then blue, also upside down. You're turning them upside down because the top is cut, the cake will spread, mix in with the frosting. It's not a bad thing, but it's sloppy.
I would use white icing inside and chocolate on the outside and let it be brown... Dying chocolate is hard. And the thing about dye, your body will pass it. Guess what happens when you consume a lot of red dye? Red poop. Guess what happens when your child consumes a lot of red dye? You have to explain to him or her that they aren't bleeding from the inside. That's not really a conversation you want to have. Green poop is fun too. So yeah, easy on the dyes, and if you're making someone a cake with a lot of dye, you want to warn them.
For piping (the art on the top) you could get a piping kit (craft stores sell this stuff, Wilton's is the big name in cake supply... In fact if you want more details on the frosting, their site has the recipes for both. Buttercream and chocolate buttercream. If you want to save money, cut the smallest hole in a quart size bag, put your icing in it, tie the opposite end, and twist the bag forcing the icing out. Gently twisting and squeezing, draw like it's a pen. (You can also get tubes of icing that are already dyed, and they have a narrow tip, so you just open it and start, real easy.)
It sounds like a lot, but once you get the fundamentals of baking down, it's easy to envision a project and figure out how to make it work. For example, if six cakes high seems daunting, make two cakes. After leveling the cakes, level them again at the middle. This would not be easy with a knife. You would want a cake leveler. Then you still have six cakes, but they're half height, so instead of your cake being a foot high, it's more like 6" high.
Source: Wife is a baker, and I've learned a lot. ;)