Cook the blackberries with sugar over medium heat for 5 to 7 minutes, stirring until soft and juicy. Blend until smooth, strain out the seeds, and cool the puree completely before adding it to the batter.

Heat the oven to 350°F and prepare three 8-inch round cake pans with parchment and a thin coating of butter. Whisk the flour, cocoa powder, baking powder, baking soda, and salt in a medium bowl.

Beat the butter and sugar until pale and fluffy, then add the eggs one at a time. Mix in the vanilla, cooled blackberry puree, and purple gel coloring until evenly combined.

Add the dry ingredients in three additions, alternating with the buttermilk in two additions. Mix only until no dry streaks remain, because excess mixing can make the cake dense.

Divide the batter evenly among the prepared pans and smooth the tops. Bake for 25 to 30 minutes, or until a toothpick inserted in the center comes out with a few moist crumbs.

Cool the cakes in their pans for 10 minutes, then turn them onto wire racks and remove the parchment. Let the layers cool completely, then wrap and chill them for at least 30 minutes for easier assembly.

Beat the cream cheese and butter until smooth, then gradually mix in the sifted powdered sugar, vanilla, and salt. Continue beating briefly until creamy, but stop as soon as the frosting is smooth to prevent it from becoming loose.

Place one cake layer on a serving plate and spread it with frosting, repeating with the remaining layers. Cover the cake with a thin crumb coat, chill for 20 minutes, then apply the final frosting layer and decorate with berries and edible flowers.