**Prep:** Preheat the oven to 350°F. Spray three 6-inch cake pans with non-stick spray and line the bottoms with parchment paper.
**Mix Dry Ingredients:** In a medium bowl, whisk together the cake flour, baking powder, baking soda, and salt. Set aside.
**Cream Butter and Sugar:** In a large mixing bowl, cream together the softened butter and granulated sugar with an electric mixer on high speed until fluffy, about 3-4 minutes.
**Add Wet Ingredients:** Add the egg whites, vanilla, and coconut extract to the butter mixture. Beat on medium-high speed until smooth and pale, about 2-3 minutes, scraping the bowl as needed.
**Combine:** Mix in the coconut milk and sour cream on medium speed until just combined.
**Add Dry Ingredients:** Gradually add the dry ingredients to the wet mixture, mixing on low then medium speed until the batter is smooth.
**Bake:** Divide the batter evenly among the prepared cake pans. Bake for 28-32 minutes, or until a toothpick inserted in the center comes out clean.
**Cool:** Let the cakes cool in the pans for 10 minutes, then transfer to a cooling rack to cool completely.