1. Prepare cake mix according to package directions, making 24 2 1/2-inch cupcakes; cool completely.
2. Puree 1 cup of the blackberries in a food processor or blender. Pour puree into a bowl through a fine mesh sieve to remove seeds. You may need to work puree with a spatula to help it through the sieve.
3. In a large mixing bowl cream the butter with an electric mixer on medium to high speed until it is light and fluffy, about 2 minutes. Add the strained blackberry puree, 3 cups of the powdered sugar and the salt. Beat on low until sugar begins to incorporate into the butter, then increase speed to medium-high to thoroughly mix. Add the remaining powdered sugar, a little at a time, until frosting reaches your preferred consistency.
4. Use a large star tip to pipe the frosting onto prepared cupcakes. Chill for 1 hour. Top each with a blackberry.