Beat the eggs in a deep bowl. Add the sugar, oil and flour and beat well. Add the baking powder, vanilla, lemonade and grated lemon rinds. Stir well to obtain a homogeneous mixture.
Pour it into a cake form that you've oiled and floured ahead of time. Bake in a preheated 356°F (180 °C) oven until ready. Serve sprinkled with powdered sugar.