Preheat the oven to 375°F. Line two baking sheets with parchment paper or silicone baking mats.
In a large mixing bowl, combine 1 white cake mix, 2 eggs, and ⅓ cup vegetable oil. Stir until a thick dough forms. Add red food coloring and mix until the dough reaches your desired shade.
In a second large mixing bowl, combine the remaining white cake mix, 2 eggs, and the remaining ⅓ cup vegetable oil. Stir until a thick dough forms, then mix in blue food coloring until evenly colored.
Scoop the dough into balls using a medium cookie scoop. Roll each dough ball in ½ cup powdered sugar until completely coated.
Place the cookies on the prepared baking sheets, leaving about 2 inches between each cookie.
Gently flatten each cookie slightly with the bottom of a drinking glass.
Bake for 8 to 10 minutes, or until the edges are just beginning to turn lightly golden.
Bake for 8-10 minutes until cookies brown slightly on the edges.
Let the cookies cool on the baking sheet for 5 minutes, then transfer them to a wire rack to cool completely before serving or storing.
Store the cookies in an airtight container at room temperature for up to 5 days.