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Preheat the oven to 350 degrees. Spray 2 8-inch round cake pans with cooking spray and set pans aside.
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Combine the cake mix, pudding mix, vegetable oil, sour cream, milk, and egg whites in a large mixing bowl. Beat on medium speed for 2 minutes, or until well combined. Pour half of the batter into a second mixing bowl and mix blue food coloring into one of the bowls to achieve your desired shade of blue.
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Drop a large spoonful (about 2 tablespoons) of white batter into one of the prepared pans. Top that with a large spoonful of blue batter, and continue layering the batter until you’ve used half of each color. Jiggle the pan occasionally to even the batter out. Repeat with the second cake pan and the remaining batter.
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Bake cake layers for 30 to 34 minutes, until a cake tester inserted into the center of the cakes comes out clean. Cool in pans for 20 minutes, then carefully invert onto a wire rack to cool completely.