Preheat your oven to 325 degrees. Spray three 8-inch round pans with nonstick spray, line the bottom of each pan with parchment paper and spray again. Set aside.
In a medium bowl or measuring cup, combine and stir the egg whites, whole egg and the vanilla. Set aside.
In a bowl of an electric mixer, fitted with a paddle attachment, combine the dry ingredients together on low speed for 30 seconds.
With the mixer on low speed, add the butter one piece at a time, about every 10 seconds.
Once all the butter is added, turn the mixer to medium-low speed and add the egg mixture in three additions, scraping the bowl down between each addition. Mix just until incorporated.
Using a kitchen scale, divide the batter into three portions, in three separate bowls.
In the first bowl, fold in 1/3 cup buttermilk.
In the second bowl, fold in 1/3 cup raspberry puree and 1 teaspoon raspberry emulsion.
In the third bowl, fold in 1/3 cup blueberry puree and 1 teaspoon blueberry emulsion.
Pour each of the different cake batters into their own cake pan, spreading evenly with a small offset palette knife.
Bake until a cake tester or toothpick comes out with a few crumbs when inserted into the center, about 25 to 30 minutes. Check cake at 23 to 25 minutes or a couple minutes before, and then set the timer for 2 to 3 minute intervals if the cake needs to bake longer. You're looking for a few moist crumbs to come out on the toothpick when inserted into the center of the cake.
Let the cake layers cool on racks for 10 minutes before inverting onto greased wire racks. Gently turn the cakes back up so the tops are up and cool completely.
Once the cakes are cooled completely, level the tops if needed.
Wrap each cake layer with plastic wrap and chill in freezer for at least an hour before using. The cake layers can be stored for up to a few days wrapped once in plastic wrap and frozen. To store longer than a few days, wrap twice in plastic wrap, then in foil, and seal in a zip-lock bag.