Heat oven to 180°C (170°C for dark or nonstick pan). Grease or spray bottom and sides of 33x23cm pan.
Make and bake cake mix as directed on the box for 33x23cm pan. Cool in pan for 10 minutes; remove from pan to cooling rack. Cool completely, about 1 hour. Refrigerate or freeze cake for 1 hour or until firm.
Meanwhile, in small bowl for each color, tint 225 grams frosting red, 225 grams frosting yellow and 150 grams frosting blue with food colors. Leave remaining frosting white.
Using serrated knife, cut rounded dome from top of cake to make flat surface; place cake cut side down. Cut cake crosswise into thirds. Cut one of the thirds in half crosswise to make 2 squares. Place cake pieces on tray.
To seal in crumbs, frost top and sides of 1 square cake with thin layer of blue frosting and 1 square cake with thin layer of white frosting. Frost 1 rectangular cake with thin layer of yellow frosting and 1 rectangular cake with thin layer of red frosting. Refrigerate or freeze 30 to 60 minutes to set frosting.
Add final coat of frosting to each cake. Frost 4 marshmallow halves with blue frosting; place in square design on blue cake. Frost 4 marshmallow halves with white frosting; place in square design on white cake. Frost 8 marshmallow halves with yellow frosting; place on yellow cake. Frost 8 marshmallow halves with red frosting; place on red cake. Store loosely covered.