Preheat oven to 350 degrees F. Butter and line with parchment three 8-inch round cake pans.
Whisk together the flour, baking powder and salt in a bowl.
In a mixer beat the butter and sugar with paddle attachment until fluffy and white.
Add in the eggs one at a time, increase speed of mixer after each egg is added. Add in the vanilla.
Lower the speed and add the flour mixture and the milk, in alternating additions. End with flour.
Divide batter equally between three bowls, about 1 1/2 cups per bowl. Add in 1/3 cup of rainbow sprinkles per bowl. Gently stir in the sprinkles. Pour batter into the three prepared pans.
Bake in oven for about 25 minutes, about 1/2 way thru rotate pans. DO NOT OVER BAKE. Test with a toothpick,
Remove cakes from oven and let cool in pans until cool enough to the touch to invert and remove from pans. Cool cakes on cooling rack until fully cooled.