Preheat your oven at 350 degrees.
Grease three 8 inch round cake pans, line with parchment paper rounds, then grease the parchment paper with baking or cooking spray
Whisk the flour, baking powder, baking soda, and salt together in a medium bowl Set aside.
Using a stand mixer or hand mixer fitted with whisk attachment, beat the butter and sugar together on high speed until smooth and creamy. Scrape down the sides and up the bottom of the bowl with a rubber spatula as needed.
Beat in the eggs one at a time and vanilla extract on medium speed until combined, about 2 minutes. Scrape down the sides and up the bottom of the bowl as needed.
With the mixer on low speed, add the flour mixture just until combined. With the mixer still running on low, add the milk, vegetable oil, lemon zest, lime zest, lime juice and lemon juice and mix just until combined. You may need to whisk it all by hand to make sure there are no lumps at the bottom of the bowl. The batter will be a little thick.
Pour batter evenly into the prepared pans. Bake for around 25 minutes or until the cakes are baked through. To test for doneness, insert a toothpick or wooden skewer into the center of the cake. If it comes out clean, it’s done. Allow cakes to cool completely in the pans set on a wire rack.
Wrap the cakes in cellophane wrap and store in the refrigerator for an hour, overnight is best. When placing them in the refrigerator, place them upside down as this helps flatten the top. The cakes must be completely cool before frosting.