Preheat the oven to 350 degrees F (175 degrees C). Line the bottoms of two 9-inch cake pans with parchment paper and lightly grease the sides.

Beat sugar, butter, and oil together in a large bowl with an electric mixer until creamy and well combined. Add eggs, 1 at a time, beating well after each addition. Stir in vanilla extract.

Combine flour, baking powder, and salt together in another bowl. Alternate mixing flour mixture and buttermilk gently into the butter mixture with a spatula, mixing until just combined after each addition; the batter should be smooth and completely combined but avoid overmixing. Divide batter evenly between the prepared pans.

Bake in the preheated oven until the surface springs back to the touch and a toothpick inserted into the centers comes out mostly clean with a few moist crumbs but no wet batter, 30 to 35 minutes.