Beat sugar and butter together in a large bowl with an electric mixture until creamy. Sift in flour. Add baking powder and vanilla; beat until well-blended. Add eggs; beat until batter is smooth. Divide batter between two 9-inch nonstick round pans.
Bake in the preheated oven until cake layers rise and turn golden, about 25 minutes. Invert onto wire racks and cool completely, about 30 minutes.