Preheat oven to 350°F (177°C). Line the bottom of 3 8-inch cake pans then, spray it with baking non-stick spray.
In the bowl of a stand-up mixer, combine the butter *12 tablespoons), 1 3/4 cups of sugar, and the vanilla (1 1/2 teaspoons), using medium speed for 5 minutes, scraping down the bowl, until the mixture is light and fluffy. Mix in the egg yolks (8 large), one at a time, mixing just until the yellow disappears, before adding the next.
In another mixing bowl, whisk together flour (3 cups), salt (1 teaspoon), baking powder (3/4 teaspoon), and baking soda (3/4 teaspoon). Turn the stand-up mixer on low, and alternate adding the flour mixture then the sour cream (1 cup), to the butter mixture, one-third of each at a time, allowing them to just incorporate before adding the next. When finished with adding both, turn the mixer on medium speed and mix for 2 minutes.
Pour the batter into a clean mixing bowl. Wash and dry the bowl of the stand-up mixer and fit it with the whisk attachment. Add the egg whites (8 large) and beat on medium speed for 5 minutes until opaque white and foamy. Add the remaining 1/4 sugar and continue to beat on medium until soft peaks form. Gently fold into the batter in 3 additions.
Scrape the batter evenly into the prepared cake pans. Bake in preheated ovens, rotating pans halfway through, until they are lightly golden and a toothpick inserted in the center of the cake comes out clean, about 30-35 minutes.
Allow cakes to cool, in pans, and set on a wire baking rack for 10 minutes. Remove cakes from pans and cool completely on the wire rack, for about 3 hours.
When cooled, brush the tops and sides of each cake layer with about 2 tablespoons of simple syrup per layer.