Trim cake layers level (see tier heights below). For each tier: Set 1 layer on foam board. Spread with buttercream (see amounts below). Add second layer (for 14-inch tier, repeat for third). Spread buttercream over top and sides; chill until firm, 30 minutes to 1 hour.
Place candy for each layer (see amounts below) in a ziplock bag, and crush with the end of a rolling pin or the smooth side of a meat mallet. Sift out dust.
Working with one tier at a time, apply a thick, smooth coat of buttercream (see amounts below). Immediately press crushed candy into the still-wet buttercream on the sides of the tier, a handful at a time, to cover evenly (reserve 1/3 cup, or 2/3 cup for 14-inch tier, to sprinkle on tops of tiers).
Assemble the cake: Place 14-inch tier on a 16-inch cake stand. Insert 7 dowels into tier, arranging 1 in the center and the rest evenly spaced about 2 inches from edge. Mark height of cake on dowels; remove, trim to be level with top of cake (but all the same length), and reinsert. Repeat for all tiers, inserting 5 dowels in the 12-inch tier. Stack tiers largest to smallest. Sprinkle reserved candy over tops of tiers.
Tier heights: 14-inch tier, trim each cake layer to 1 1/4 inches high for a finished height of 5 inches; 12-inch, trim to 1 1/4 inches high, finished height of 3 inches; 10-inch, trim to 1 3/4 inches high, finished height of 4 inches; 8-inch, trim cake layer to 2 inches high, then split horizontally to make 2 layers, for a finished height of 2 1/2 inches; 6-inch, trim to 1 1/2 inches high, finished height of 3 1/2 inches. Buttercream and candy amounts (the brand we used comes in tins that hold roughly 1/3 cup): 14-inch tier, 10 cups buttercream for filling (divide between layers), 7 1/2 cups buttercream for frosting, 3 cups candy; 12-inch, 3 cups filling, 4 1/2 cups frosting, 2 cups candy; 10-inch, 2 1/2 cups filling, 3 1/2 cups frosting, 1 2/3 cups candy; 8-inch, 1 1/4 cups filling, 2 1/2 cups frosting, 1 1/3 cups candy; 6-inch, 3/4 cup filling, 2 cups frosting, 1 cup candy.