For the Rainbow Cake Layers:
Preheat your oven to 350°F (175°C). Prepare two or three 8-inch round cake pans by greasing them with baking spray or butter, then lining the bases with parchment paper to ensure easy release.
In a large mixing bowl, sift together the flour, sugar, baking powder, baking soda, and salt until well combined.
In a separate bowl, whisk the eggs, vegetable oil, milk, and vanilla extract until the mixture is smooth and well blended. Gradually pour this wet mixture into the dry ingredients, whisking until the batter is lump-free and consistent.
Divide the batter evenly among six bowls. Add food coloring to each bowl to create the different colors: red, orange, yellow, green, blue, and purple. Stir until the color is evenly distributed in each batch. Pour one colored batter into a prepared cake pan. Keep the remaining bowls in the fridge until you are ready to bake them. This will prevent premature activation of the baking powder.
Bake each layer for approximately 20 minutes or until a toothpick inserted into the center comes out clean. Allow the cakes to cool in the pans for 10 minutes before transferring them to a wire rack to cool completely. Repeat the process for the remaining batters, ensuring you re-grease and line the pans between batches.