Preheat oven to 350F if using an aluminum tube pan, or 325F if using a dark nonstick tube pan. Lower the oven rack to the lowest position.
In a small mixing bowl, whisk together cake mix and cocoa powder until combined. Set aside.
In the bowl of a stand mixer fitted with the whisk attachment (or in a large mixing bowl with a handheld electric mixer), beat the egg whites at high speed until soft peaks form.
Add the cake mix/cocoa powder mixture to the egg whites, along with the vanilla extract and water. Mix on low speed for about 30 seconds, then scrape down the sides of the bowl. Mix on medium-high speed for another minute, until the batter is glossy.
Pour the batter into an ungreased tube pan, spreading it evenly. Bake in preheated oven for 45-55 minutes, or until the surface of the cake is not even slightly sticky to the touch.
Remove from oven and turn the pan upside down to allow the cake to cool. The cake should be elevated off the surface (I use a tube pan with "feet" for this purpose, but some people invert their pan on a heatproof glass bottle).
Once cake is completely cool, slide a knife around the edges of the cake and remove from the pan onto a serving plate. If desired, dust the top of the cake with powdered sugar before slicing and serving.
Notes
I like to use a tube pan with feet and a removable center for easy cooling and removal of the cake, like this one.
It's important to not grease the pan, as this helps the cake batter rise better when baking.
This cake is fantastic served with fresh berries and whipped cream! It's also delicious with fruit compote and a scoop of ice cream.
I find that a serrated knife is best for cutting angel food cake.
Leftover cake can be stored at room temperature in an airtight container or tightly covered with plastic wrap for about 3-5 days.