Mix frosting with 1 to 2 drops food coloring to tint it blue. (We like to use the all-natural dyes from colorkitchenfoods.com.) Set aside.
Trim domes from tops of cakes. Transfer one cake layer to serving platter, and spread with about 1 1/4 cups frosting. Top with second cake layer and coat with remaining frosting, spreading smooth.
Cut licorice crosswise into scant 1/4-inch pieces. Arrange candy pieces following the pattern.