Preheat the oven to 350°F / 175°C. Butter and generously coat a 12 cup capacity bundt pan with sugar or flour.
In a medium sized bowl, whisk together the flour, baking powder, and salt. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment (or with a hand mixer), beat together the butter, oil, and brown sugar for 5 minutes until light and fluffy.
Scrape down the sides of the bowl, and add in one whole egg at a time, beating for 20 seconds between each addition until well combined. Add in both egg whites and the vanilla, and beat until well combined.
Alternate between adding in the flour mixture and the sour cream and milk. Fold in ⅓ of the flour mixture, then ½ of both the sour cream and milk. Then, fold in ½ of the remaining flour mixture, all of the remaining sour cream and milk, then the remaining flour mixture.
Prepare three small mixing bowls. To each bowl, add one of the cocoa powders.
To each bowl of cocoa powder, whisk in ~36g (2 ½ tbsp.) of hot espresso.
To each bowl, add in 225g (1 c.) of the vanilla cake batter. Gently fold the cake batter into each of the cocoa powder mixtures until just combined.
Evenly spread 260g (1 c. + 2 tbsp.) of the vanilla batter into the prepared bundt pan. Place dollops of the natural cocoa powder batter over the vanilla and gently spread it into an even layer.
Top with another layer of vanilla batter, followed by the dutch processed cocoa powder batter.
Top that layer with another layer of vanilla batter, followed by the black cocoa powder batter, and the remaining vanilla batter.
Bake the cake for 50-60 minutes, until a knife inserted in the bundt comes out with only a few moist crumbs.
Allow the cake to cool in the pan for 10-15 minutes. Once the pan is cool enough to touch, flip the cake out onto a cooling rack and let it cool completely before frosting.