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Preheat oven to 350 degrees. Spray two 9-by-13-inch baking pans with cooking spray. Line with parchment, leaving an overhang on long sides. Spray parchment. Flour pans, tapping out excess.
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Sift together cocoa powder, flour, sugar, baking soda, baking powder, and salt in a large bowl. Mix in eggs, buttermilk, water, oil, and vanilla until smooth. Divide batter between pans. Bake, rotating halfway through, until tops of cakes spring back when pressed and a toothpick comes out clean, about 35 minutes. Let cool completely, then lift cakes from pans using parchment. Remove parchment.