Preheat oven to 325° and grease and flour a 12-cup Bundt pan.
In a big mixing bowl, beat together the cake mix, oil, egg whites, and water on low speed for 30 seconds, scraping bowl as needed. Increase speed to medium and beat for 2 minutes, scraping bowl as needed.
Pour 1⅔ C. batter into a small bowl; stir in 1 extract and up to 12 drops food coloring. Pour 1⅔ C. batter into a second small bowl; stir in chocolate syrup. Keep the remaining batter plain. Pour a thin layer of each batter into prepped pan, one on top of the other. Repeat until you've used all the batter. Run a knife or chopstick carefully through the batter in a zig-zag or swirled pattern. (Or simply make three thicker layers.)
Bake for 35 to 45 minutes, until a toothpick inserted in the center comes out clean. Cool in the pan for 10 minutes. Invert pan on a wire rack to remove cake. Cool completely before slicing. Warm the frosting to a drizzling consistency and drizzle over the cake if you'd like.