Preheat oven to 325 degrees and set aside an ungreased 10-inch tube pan.
Place the egg whites and cream of tartar in a medium mixing bowl and beat with an electric mixer on high until stiff peaks form, about 2-3 minutes.
Place the cake mix, egg yolks, water, oil, coffee powder, and vanilla in a mixing bowl and blend on low for 1 minute. Stop the machine to scrap down the sides with a rubber spatula then increase mixing speed to medium and beat for 2 more minutes, continuing to scrap the sides of the bowl as needed. Turn the beaten egg whites on top of the batter and with a rubber spatula fold the whites in to the batter until the mixture is combined but still light. Pour the batter into the prepared pan, smoothing out the top and place the pan in the oven.
Bake the cake until it springs back when pressed with your finger and a toothpick inserted in the center comes out clean and without batter, about 48 to 52 minutes. Remove the pan from the oven and immediately turn it upside down over the neck of a glass bottle. Run a long, sharp knife around the edge of the cake and invert it onto a serving platter so it is right side up.