Preheat the oven to 350°F. Line 3 (8-inch) cake pans with parchment paper, then grease and set aside.
In a medium bowl, whisk cake flour, salt, baking powder, and baking soda, and set aside.
In a large bowl or the bowl of a stand mixer, beat butter and sugar until light and fluffy. Add the whole eggs, egg whites, and vanilla, and mix until smooth.
With the mixer on low, gradually add the dry ingredients, until well combined, scraping down the sides of the bowl as needed. Pour in buttermilk and mix until combined.
Divide the batter into 3 bowls and add red food coloring to one and blue to another, keeping the third white. Pour into three prepared cake pans.
Bake for 25-30 minutes, until lightly browned around the edges, and a toothpick inserted in the center comes out clean. Remove from oven and let cool completely.