Preheat the oven to 350 degrees F (175 degrees C). Grease two 8-inch round cake pans.

Cream sugar and butter together in a large bowl using an electric mixer until pale and fluffy, 6 to 7 minutes. Beat in eggs, 1 at a time. Stir in vanilla extract.

Combine flour and baking powder in a separate bowl. Add to butter mixture and mix well. Stir in milk until batter is smooth. Pour evenly into the prepared pans.

Bake in the preheated oven until a toothpick inserted into the center comes out clean, about 30 minutes.