In a large bowl, whisk together the pudding mix and milk until combined. Separate pudding evenly into 3 separate bowls.
Color one bowl of pudding with the red food coloring. Mix well.
Color the second bowl of pudding with blue coloring. Mix well.
Leave the third bowl white.
Fill each paper cup with 2 Tablespoons of red pudding. Then top red pudding with 2 Tablespoons of white pudding. Top white pudding with 2 Tablespoons of blue pudding. Insert sticks into the center of each pudding cup. Place in the freezer for 8 hours or overnight.
Remove from freezer and carefully peel off paper cup. Serve!