Arrange these cupcakes to form the age that's being celebrated.
Preheat oven to 350 degrees. Line mini muffin tins with baking cups. Sift flour, sugar, cocoa, baking soda, baking powder, and 1 teaspoon salt into a large bowl. Mix in eggs, warm water, buttermilk, oil, and vanilla, scraping down sides of bowl, until smooth, about 3 minutes.
Working in batches, divide batter evenly among cups, filling each two-thirds full. Bake, rotating tins halfway through, until tops spring back when pressed with a finger, about 20 minutes. Let cupcakes cool completely on a wire rack.
Using a pastry bag fitted with a fine star tip, pipe buttercream onto cupcakes to decorate.
Unfrosted cupcakes can be stored at room temperature for up to 3 days.