Preheat the oven to 350 degrees F and spray a bundt pan generously with non-stick spray.
Place the flour, sugar, baking soda, and salt in a large mixing bowl and stir briefly to combine.
Add the buttermilk, oil, and egg whites, and mix on low speed until smooth. Scrape the bottom and sides of the bowl, and mix again for about 1 minute, to aerate the batter and develop the structure.
Place ½ teaspoon of cocoa, ½ teaspoon of vanilla, and ¼ teaspoon of vinegar in each of two small bowls.
Add the red food coloring to one of the bowls, and the blue and violet food coloring to the other. Mix about a cup of batter into each.
Place about ¼ cup of red batter into the prepared pan. Layer with white, then blue, then white again.
Repeat until the pan is filled.
Bake for approximately 35-50 minutes*, or until a tester inserted in the thickest part of the cake comes out clean or with a few moist crumbs.
Cool for 15 minutes, then invert onto a wire rack to cool completely.
Place the powdered sugar and Greek yogurt in a small bowl and stir to combine.
Pour the glaze over the cake and allow to dry.
Fill the center of the cake with strawberries and blueberries, and serve.