Prep your oven and pans. Position a rack in the center of the oven and preheat the oven to 350°F. Generously spray three 8-inch round cake pans with cooking spray and line the bottom of each with a parchment paper circle. Spray the parchment, too.
Make the cake batter. Place the Pillsbury Funfetti cake mix in a large bowl. Use a tall glass to press down into the center of the mix to make a "well".
Pour the water, oil, and egg whites into the well and mix with a rubber spatula until just combined. At this point, your batter will likely still be lumpy—that's okay, I promise!
Set a small bowl on a digital scale and tare it to “0”. Pour batter into the pan until the scale registers 11 ounces (312 grams). Repeat with a second and third bowl. If necessary, redistribute any leftover batter evenly between the three bowls. Each bowl should contain between 11 ounces (312 grams) to 11.15 ounces (316 grams) of batter. Add blue food coloring, either with a ¼ teaspoon measure or 1 to 2 generous drops at a time, to one bowl of cake batter. Mix with a small rubber spatula or spoon until completely combined. Keep adding food coloring until the cake batter is bright blue and very saturated. Once done, pour the batter into one of the prepared cake pans.
Add purple food coloring, either with a ¼ teaspoon measure or 1 to 2 generous drops at a time, to a second bowl of cake batter. Mix with a small rubber spatula or spoon until completely combined. Keep adding food coloring (however, no more than 1 teaspoon of food coloring) until the cake batter is bright purple and very saturated. Once done, pour the batter into one of the prepared cake pans.
Add green food coloring, either with a ¼ teaspoon measure or 1 to 2 generous drops at a time, to the last bowl of cake batter. Mix with a small rubber spatula or spoon until completely combined. Keep adding food coloring (however, no more than 1 teaspoon of food coloring) until the cake batter is bright green and very saturated. Once done, pour the batter into the remaining prepared cake pans.
Bake the cakes. Bake for 16 to 18 minutes, or until the top of each cake bounces back when gently pressed. A skewer inserted into the center of the cake should come out with a few crumbs attached. Cool the cakes in their pans on a wire rack for 20 minutes, then turn out onto the wire rack and cool completely. The cakes can be stored unfrosted, wrapped tightly in plastic wrap, at room temperature for up to 2 days and in the freezer for up to 3 months.