Preheat oven to 350°F (175°C). Grease three 8 inch (20 centimeter) cake tins. Line the bottoms with parchment paper and grease the parchment. Set aside.
In a large bowl sift together the flour, baking powder and salt; set aside.
Using an electric mixer or in the bowl of a stand mixer fitted with the paddle attachment beat the butter, Redpath® Granulated Sugar and Redpath® Golden Yellow Sugar on medium speed until pale and fluffy, 4 minutes.
Add the eggs one at a time, allowing each egg to fully incorporate before adding the next.
Mix in the lemon and vanilla extracts.
Reduce speed to low and alternate adding 1/3 the flour mixture to the butter mixture with 1/2 the milk, scraping down the sides of the bowl as necessary, until all ingredients are combined.
Split batter evenly into 6 bowls (each bowl should have about 260 millilitres (280 grams) of batter.
Colour each batter a different rainbow shade. Start adding colouring a couple of drops at a time until desired shade is reached (the colour of the batter will be the same after baking).
Scrape three colours of batter into the prepared pans and smooth each with an offset spatula (take care to clean spatula between colours).
Bake in oven until cake is set in the middle and springs back when gently pressed, about 12 to 14 minutes.
Remove from oven and cool 5 minutes. Run a sharp paring knife around the edge of the cake. Cool 5 minutes more and using oven mitts or a teatowel to hold the pan if still hot, carefully turn cakes out onto a cooling rack.
Wash and dry cake pans. Repeat greasing the pans, lining the bottom with parchment and greasing the parchment.
Scrape the remaining 3 colours of batter into the pans, smooth and bake as directed.
Allow cakes to cool completely before assembling.
Using an electric mixer or in the bowl of a stand mixer fitted with the paddle attachment beat the cream cheese and butter on medium speed until smooth.
Beat in the the Redpath® Icing Sugar about a cup a a time until smooth. Add in the lemon juice and vanilla.
Level the tops of the cakes using a serrated knife.
Place a small dollop of frosting on a cake stand or plate and invert the violet layer over top.
Using an offset spatula, spread the cake with about 2/3 cup (145 g) of frosting. Repeat layering with frosting the blue, green, yellow, orange and red cakes.
Cover the sides and top of the cake with a thin layer of frosting and chill in refrigerator for 15 minutes.
Spread the remaining frosting evenly over the top and sides of the cake.
Chill cake for 30 minutes in refrigerator before slicing and serving.
*Coconut or almond extract may be used in place of the lemon extract.
*Be sure to use gel food colouring. Traditional liquid food colouring may add too much extra moisture to the batter.