Preheat the oven to 350°F. Line the bottoms of 3-9” cake pans with parchment paper and lightly spray with baking spray. Set aside.
In a large mixing bowl, combine cake flour, regular flour, baking powder, baking soda, and salt. Set aside.
In the bowl of a stand mixer fitted with a paddle attachment, combine sugar and butter. Beat on medium speed for 2 minutes.
Stop the mixer and scrape down the sides of the bowl with a rubber spatula, then add egg whites. Mix until just combined.
Add sour cream, coconut extract, and vanilla. Mix to combine.
Add coconut milk and mix. Slowly add in the flour mixture and mix until just combined.
Add shredded coconut and mix to incorporate.
Divide the batter into the 3 prepared cake pans. Bake for 28 minutes, or until a toothpick inserted into the centers comes out clean or with a few moist crumbs.
Once baked, remove from the oven and set onto a wire cooling rack to cool completely.