In the bowl of a large electric mixer, beat the butter until smooth.
Add the cream cheese, and beat further until the butter and cream cheese are fully incorporated and smooth.
With the mixer on low, add the powdered sugar, one cup at a time.
Again, with the mixer on low, add the blackberry puree, one tablespoon at a time.
Continue beating, increasing speed to medium for about 30 seconds.
Depending on the temperature in your kitchen, and the moisture in your berries, the frosting may be on the soft side. I put the whole bowl of finished frosting in the refrigerator for about 1 hour to help the frosting firm up. If needed, you could add an additional cup of powdered sugar.
Frost cupcakes as desired, or layer cupcakes and frosting in a jar.