Reserve 8 blackberries from 1 pint. Cook the rest of the berries with 2 tablespoons cane sugar in a saucepan over high heat until the berries are just starting to break down. Transfer to a bowl and let sit in another bowl of ice water to chill. Blend the cooled berries, 1 pint vanilla ice cream, 12 ounces pomegranate juice and 1 cup milk until thick and creamy. Pour into tall glasses and top with the reserved berries.