Special equipment: four 8-inch round cake pans; a cake stand; a cake turntable, optional
For the cake: Preheat the oven to 350 degrees F. Coat four 8-inch round cake pans with cooking spray and dust with flour, tapping out the excess. (If you don't have 4 pans, make 1 box of cake mix at a time and use half of the food coloring in each batch.)
Prepare the cake batter according to the package directions. Divide the batter among 3 bowls. Add the green food coloring to one, the pink to the next and the yellow to the last. Create a tie-dye pattern by randomly adding a quarter-cup scoop of different color batters to the pans, dividing the batters among the 4 prepared pans. Use a toothpick to swirl the colors. Tap to release air bubbles and bake, rotating the pans from top to bottom halfway through baking, until a tester inserted in the center comes out clean, 25 to 28 minutes. Let cool on a rack for 10 minutes, then remove from the pans and cool completely.
For the buttercream: Beat the butter and salt in a large bowl with an electric mixer on medium speed until smooth and light, about 1 minute. Add the confectioners' sugar and beat on low to incorporate, then increase the speed to medium high and beat until fluffy, 1 to 2 minutes. Beat in the vanilla and then the milk, 1 tablespoon at a time, until the frosting is easily spreadable.
Cut the domed tops from the cakes to make them flat. Frost the top of one cake layer with about 1/2 cup frosting. Set another layer on top and frost again. Repeat with the third layer, then end with the last layer bottom-side up on top. Coat the cake with a very thin layer of frosting to crumb coat, then chill until set, about 15 minutes.
Set the cake on a cake stand and spread the remaining frosting on the cake in a smooth layer. Freeze at least 4 hours and up to overnight.
For the glaze: Combine the marshmallows and butter in a microwave-safe bowl. Microwave on high in 30-second intervals, stirring in between each, until the mixture is smooth and melted, 1 to 2 minutes. Slowly stir in the tonic water; the glaze should be pourable, but still coat the back of a spatula.
Divide the glaze among 3 bowls. Stir in the food coloring: green in one bowl, pink in the next and leave the last bowl white.
Place the cake on a cake turntable with a baking sheet underneath or balance the cake on a large soup can with a baking sheet underneath. Pour the glazes over the cake in a circular pattern, starting at the edges and working your way into the middle, alternating the colors and making sure to cover the whole cake. Let the glaze drip off for about 15 minutes, then transfer to the fridge to set.
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