Preheat your oven to 350 degrees. Spray a 9 inch springform pan with cooking spray and set aside.
In a large bowl, whisk together the flour, baking powder, and salt. Set aside.
With your mixer on medium, mix together the butter and sugar until light and fluffy.
Mix in the eggs (one at a time) and then the vanilla until well combined.
Slowly mix in the flour mixture until well combined, with your mixer set to low. Scrape down the paddle and the sides of the bowl as necessary.
Divide the dough evenly into six bowls and mix with the colors of the rainbow. Starting with the purple dough, press it into the bottom of the pan as evenly as possible. Work your way up through the rainbow dough. The layers will not be completely even or perfect, but that's okay.