Make cakes 1 day in advance. Prepare cake batter. Bake and cool three 6 in. cake layers and Minion cakes (10 needed for cake).
Decorate Minions cakes also 1 day in advance. Prepare royal icing. Tint small portions black, gray and brown; reserve a small portion white. Tint remaining royal icing yellow and blue.
Use spatula and yellow royal icing to ice back of mini cake and top 3/4 of front smooth. Place on parchment-covered cake board. Position licorice hair. Let icing crust slightly, about 20 to 30 minutes.
Use 12 in. decorating bags to decorate mini cakes. Use tip 8 and blue icing to fill in overalls; pipe outline straps. Use tip 8, decorating bag and yellow icing to pipe outline arms. Use tip 12 and blue icing to pipe pull-out legs. Use tip 8, decorating bag with coupler and black icing to pipe dot gloves and shoes. Use tip 8 and white icing to pipe in eyes. Use tip 4 and brown icing to pipe dot pupils. Use tip 4 and gray icing to pipe outline lenses. Use tip 4 and black or gray icing to pipe zigzag glasses frames. Use tip 2 and black icing to pipe outline smile, dot irises and details on overalls.
Insert lollipop stick in bottom of four mini cakes, leaving 5 in. extended at bottom to be inserted in cake top. Let cakes dry on parchment-covered cake board overnight.
Ice 6 in. cake. Prepare buttercream icing. Tint 1/4 icing orange; tint remaining yellow. Level, fill and stack 6 in. cakes on same-size cake circle for a 3-layer cake, 5 in. high. Place on turntable. Use tip 1D, a 16 in. disposable decorating bag and orange buttercream icing to pipe one band around bottom of cake. Use tip 1D and yellow buttercream icing to cover remainder of cake side and top. Use icing smoother to smooth.
Assemble cakes. Use yellow buttercream icing to attach two mini cakes with sticks back to back. Insert in cake top. Insert remaining cakes on sticks using the first two cakes for support. Attach remaining mini cakes with icing to cake side.