Preheat the oven to 350°F (175°C). Grease and flour three 9-inch round cake pans.
In a large bowl, cream together the softened butter and granulated sugar until light and fluffy.
Add the eggs one at a time, mixing well after each addition, then add the milk and blackberry puree.
In another bowl, whisk together flour, baking powder, baking soda, and salt.
Gradually add the dry ingredients to the wet mixture, mixing just until combined.
Divide the batter evenly among the prepared pans and smooth the tops.
Bake for 25-30 minutes, or until a toothpick inserted in the center comes out clean.
Allow the cakes to cool in the pans for 10 minutes, then transfer to wire racks to cool completely.
While the cakes cool, prepare the frosting by creaming the softened butter with powdered sugar.
Mix in the blackberry puree and heavy cream until smooth and well combined.
Once cooled, place one cake layer on a serving plate and spread a layer of frosting on top.
Repeat with the second cake layer and finish by placing the third layer on top.
Frost the top and sides of the cake with the remaining blackberry frosting.
Garnish with fresh blackberries on top for decoration.
