Decorate cake sides. Carefully ice the open spots on the cake sides with black icing leaving the top uniced. Smooth the icing with the spatula, and over a piece of parchment or a sheet pan, sprinkle the black sprinkles over the stripes to coat all the exposed black icing. Reserve remaining black icing.
Carefully peel off the parchment strips, revealing the uniced strips. Using even pressure, pipe tip 233 pull-out fur starting with purple icing on the bottom, orange in the middle, and the teal on the top strip going over the top of the cake.