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Preheat oven to 350 degrees. Butter round or square cake pans, and line bottoms with parchment; butter parchment, and dust with cocoa.
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Into the bowl of an electric mixer fitted with the paddle attachment, sift cocoa, flour, sugar, baking soda, baking powder, and salt. With the mixer on low, stir in eggs, 1 1/2 cups warm water, buttermilk, vegetable oil, and vanilla until smooth, about 3 minutes.
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Divide batter among prepared pans. Bake, rotating once, until tester inserted in center comes out clean, 35 to 45 minutes for 8-inch layers, depending on amount of batter.
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Let cakes cool in pans on a wire rack for 20 minutes, then remove from pans and cool completely, right side up on rack.