Preheat oven to 350 degrees. Sift flours, baking powder, baking soda, and 1 1/2 teaspoons salt into a bowl.
Beat butter and sugar with a mixer on medium-high speed until pale and fluffy, about 3 minutes. Reduce speed to medium, and add eggs, 1 at a time. Reduce speed to low, and gradually add flour mixture, alternating with buttermilk, beginning and ending with flour. Beat in vanilla.
Butter a 5-inch tart pan with a removable bottom, dust with all-purpose flour, and tap out excess. Line mini-muffin tins with mini baking cups (you'll need 75 cupcakes total).
Fill tart pan halfway with batter (about 1/2 cup), then fill each baking cup halfway with batter (a generous tablespoon each). Bake until tops spring back when lightly touched, about 12 minutes for the cupcakes and 14 minutes for the cake. Transfer pans to wire racks, and let cake and cupcakes cool completely.
Transfer 1/4 cup buttercream to a bowl, and stir in cocoa powder. Divide remaining buttercream among 3 bowls, and tint each batch a different shade of yellow or orange with gel-paste food coloring. Frost tops of cupcakes using the 3 colors. Frost top of cake with chocolate buttercream. Arrange berries over top of cake to cover and create "seeds." Arrange cupcakes around cake to create "petals," forming a sunflower shape.
Unfrosted cake and cupcakes can be stored at room temperature for up to 3 days.