Heat oven to 350°F.
Spray 12-cup fluted tube cake pan with baking spray with flour. Open first can of biscuits, and cut each into 4 pieces. Place biscuit pieces in large bowl. In small bowl, use whisk to mix 2 tablespoons of the melted butter with pink gel food color; drizzle over biscuit pieces. Stir biscuits until coated with colored butter, then toss with 2 tablespoons of the white sugar and the pink sugar.
Repeat with remaining cans of biscuits, tinting 1 batch blue and 1 batch purple.
Begin layering monkey bread in a tie-dye pattern by placing 6 to 8 pieces of same-colored biscuit pieces into 1 area of pan. Create a single layer with pink, blue, and purple-colored sections of biscuit pieces. Sprinkle half of the marshmallows on top. Place a second layer of colored biscuits, then remaining marshmallows, followed by final layer of biscuits.
Bake 30 minutes. Cool 5 minutes before turning out onto large plate.
If glaze is desired, divide frosting evenly among three small bowls. Tint 1 bowl pink, 1 blue, and 1 purple. Transfer each color of frosting to small resealable food-storage plastic bag. Cut off tiny corner of bag, and squeeze frosting out through hole to pipe onto top of warm monkey bread. Serve immediately.