Preheat the oven to 350°F (175°C). Grease and flour three 8-inch round cake pans.
In a large bowl, cream together the sugar and butter until light and fluffy.
Add the egg whites one at a time, beating well after each addition.
In a separate bowl, whisk together the flour, baking powder, and salt.
Gradually add the dry ingredients to the wet mixture, alternating with milk. Stir in vanilla.
Divide the batter evenly between the prepared pans.
Bake for 22–25 minutes, or until a toothpick comes out clean. Cool in pans for 10 minutes, then turn out onto wire racks to cool completely.