Preheat oven to 350 degrees. Line 2 muffin tins with cupcake tins. Sift flours into a bowl. Measure in rest of the dry ingredients, and whisk together, set aside.
In a food processor, pulse sugar and lime zest until finely ground. This may take a minute. Add this mixture, and butter into the bowl of a stand mixer, and whip until fluffy. Scrape down sides of bowl.
Now its time to add in egg and egg whites one at a time, mixing between additions. Next, stir in vanilla and almond extract.
Using a 2 cup measuring cup, measure in 1 cup of buttermilk, then add in the 4 tablespoons of lime juice, and stir to blend.
Working in 3 batches, alternate the buttermilk mixture and the flour mixture starting and ending with the flour mixture. Mix between each addition. Using a spatula, scrape down sides of bowl.
Spray the paper cupcake wrappers with a non stick spray. Using an ice cream scoop, or a 1/4 cup measuring cup, divide batter among the 2 muffin tins. Place each pan on a rack in the oven.
Bake 18-20 minutes, turning pans and swiping racks half way through the baking process. Check doneness by inserting a toothpick that comes out clean. Allow cupcakes to cool, but still be slightly warm when you brush with syrup.