Spray a 9" round cake pan with nonstick spray. In a small bowl, mix warm water and yeast; set aside 5 minutes.
In a large bowl, mix dry cake mix and 2 cups of flour. Add the water/yeast mixture and stir with a wooden spoon or your hands until a dough forms. Add remaining flour slowly, you may not need it all.
Place dough in a clean bowl, cover bowl with plastic wrap and let rise in a warm place until doubled, about an hour.
Once dough has risen, gently punch down, reshape into a ball and set aside a few minutes more.
Preheat oven to 400 degrees. Blend together melted butter, cream cheese, sugar and cinnamon. Divide mixture evenly into three bowls. Tint two of the bowls with the red and blue food dye.
Lightly flour a flat surface and roll dough out into a large rectangle, about 1/4" thick. Spread each color of filling length-wise across dough in stripes, getting as close to the edges as possible. Beginning with one long side of the dough, roll into a log.
Use a sharp knife to carefully cut 1'' portions of dough, then arrange cinnamon rolls into prepared pan. Bake 12-15 minutes until golden. Cool 10 minutes.
In a small bowl, whisk together powdered sugar and milk until smooth. Drizzle over cinnamon rolls.