Preheat oven to 400°F. Grease and flour three round 9-inch pans that are lined with parchment paper.
In the large bowl of a stand mixer, cream together butter and sugar on medium speed until light and fluffy, about 5 minutes.
Scrape the sides and bottom of the bowl. Add the eggs, one at a time, beating well after each addition.
Scrape the bowl again.
Sift together the cake flour, baking powder and salt. Set aside.
In a large measuring cup, whisk together the milk, coconut milk, vanilla extract and coconut extract.
With the mixer on low, alternately add the flour mixture and the milk mixture, starting and ending with the flour mixture. Mix until combined.
Scrape the sides and bottom of the bowl; mix on medium speed for about 5-7 minutes.
Divide the batter evenly between the three prepared pans. Tap on the counter once or twice to release any air bubbles.
Bake for 18-20 minutes, or until a toothpick inserted in the center comes out clean.
Let the cakes cool in the pans for about 10 minutes, then remove from the pans and cool completely on wire racks.