In a medium saucepan over low heat, cook down the blackberries with the sugar and water, stirring and smashing the berries. Continue to cook until the berries break down and the sugar fully dissolves, about 10 minutes. Remove from heat and allow to fully cool.

Strain the sweetened berry mixture through a fine mesh sieve, discarding the seeds. Chill until ready to use.

Combine whipping cream, half and half, and confectioners sugar until well mixed.

Fill popsicle molds by either alternating berry and cream mixture, or combine berry and cream mixture and then add to the molds. Freeze until solid, at least 2 hours.