In a small saucepan, bring the sugar, 1/4 cup water and two thirds of the berries to a boil. Lower the heat and simmer until the berries are very soft, 5 to 10 minutes. Strain and press through a fine-mesh strainer set over a bowl; discard the seeds. Refrigerate until cold.
Divide the ice cream among six tall 16-oz. glasses. Top with the seltzer, leaving a little space at the top of each glass. Top the sodas with the blackberry puree and garnish with the remaining berries. Serve immediately with a long spoon and a straw.