1. Preheat the oven to 350 degrees °F. Grease bundt pan.
2. Sift flour, baking powder, and salt into a bowl.
3. Beat butter and sugar together in a separate large bowl with an electric mixer until light and fluffy. Add eggs one at a time, beating well after each addition. Beat in vanilla extract.
4. Add flour mixture in batches, alternating with milk, mixing just until combined.
5. Reserve 3/4 cup batter; pour remaining batter into the prepared pan.
6. Mix cocoa into reserved cake batter until even in color.
7. Drop chocolate batter by large spoonfuls on top of vanilla batter and swirl with a knife for a marbled effect.
8. Bake in the preheated oven until a toothpick inserted into the center comes out clean, about 28 to 30 minutes. Cool briefly on a wire rack before inverting carefully onto a cooling rack. Let cool completely before icing and slicing.