Bake in a smooth round bundt pan. Cool completely.
Using a serrated knife, cut away the bottom 1/3 of the cake. The top 2/3 of the cake will be the rainbow.
Gently prop the bundt cake up and place onto cake board/plate, using good amounts of buttercream under and around the ends of the rainbow to keep it standing. Let chill for at least an hour till the buttercream is set and the cake is more sturdy.
Spread a thin crumb coat of buttercream over the entire cake. Frost the topmost edge of the rainbow in purple buttercream.
Place pink, red, orange, yellow, teal, blue and purple buttercream into piping bags fitted with a medium round tip. Pipe the colors over the face of the rainbow from one end to the other in uniform lines, starting with pink, then red, then orange, yellow, teal, blue and purple. Repeat on the other side.
Place white buttercream in a piping bag fitted with a large round tip. Pipe buttercream all around the bottom ends of the rainbow cake to make the clouds.