Preheat the oven to 350 F. In a large bowl, mix together cake mix, eggs, and vegetable oil until smooth. Divide the cookie dough between two bowls and mix one with red food coloring and one with green.
Take a small amount of each cookie dough and roll together into balls. Place one Oreo cookie in each cookie dough and roll into balls. Place cookies onto a large ungreased baking sheet at least 2-inches apart. Bake for 10-12 minutes.