Set the oven to 350 degrees F (175 degrees C). Put grease in three round pans that are 8 inches in size.
Beat together butter and sugar until they have changed color and become lighter in color. Then, add the eggs one at a time, and then add the vanilla.
Combine the flour, baking powder, and salt in a bowl. Whisk the mixture into the butter, alternating with the milk.
Pour the batter into three bowls. Stir the beet puree into one bowl, the blueberry puree into another, and leave one plain (or add mango to the third).
For a concentric reveal, pour rings of each color into the pans. Bake for 22–26 minutes. A toothpick should come out clean.
Cool completely, stack with buttercream in between, and frost the outside.