Heat oven to 350°F. Generously grease and flour a clean 34- to 39-ounce metal coffee can. Prepare cake mix according to package directions. Pour batter into prepared can and bake 55 to 60 minutes in center of oven, or until a toothpick inserted in center comes out clean. Transfer to wire rack and cool 15 minutes. Run knife around outside edge to release cake; flip onto wire rack and cool completely.
To make paintbrush, work the flour into the cookie dough until smooth. Roll dough out on foil to a 1/4-inch thickness; cut out handle shape. Transfer cutout (on foil) to baking sheet. Bake until golden brown, 8 to 10 minutes. Transfer to wire rack and cool completely. For bristles, cut 2 pieces of licorice in half lengthwise, then in thirds crosswise (for a total of 12 pieces). Spread a small amount of vanilla frosting along straight side of cookie handle and press twist pieces into frosting. Secure with a 3/4" strip of foil. Set aside to dry.
Tint 1/2 can vanilla frosting purple; set aside. Tint 1/3 cup frosting yellow and spoon into a small resealable bag; set aside.
Trim to make top of cake level. Invert onto serving platter or cutting board. With a small knife, cut a 3/4-inch deep well 1/2 inch from outer edge of cake. Remove and discard scraps. Frost sides and top edge of cake with vanilla frosting. Place a 1-inch strip of foil around bottom edge of cake.
Cut remaining 2 pieces of licorice in half lengthwise and press into top rim of cake. Sprinkle sides of cake with sugar crystals. Snip a corner from bag with yellow frosting and pipe a solid 4 x 5-inch rectangle on side of can; smooth rectangle. Pipe child's name and "Purple Passion" with black decorating icing. Press small purple candies along outer edge of yellow frosting.
To make lip of paint can, cut out a ring of foil. Press black licorice strands along bottom and top edge of cake. Press cereal loops on either side of top edge.
Heat purple frosting in the microwave for 10 to 20 seconds on high, or until slightly runny. Carefully dip the brush ends in the frosting and set aside. Pour remaining frosting into the well, dribbling it down sides of cake to make spills. Place paintbrush on top. For handle, press a piece of black licorice through cereal loops.