We chose rocket-style molds to make these multicolored treats. But you can use any you like.
In a blender, combine blackberries and 1/2 cup each sugar and cream and blend until smooth, scraping down sides as necessary. Pour through a fine-mesh sieve into a medium bowl, pressing on solids (you should have about 2 cups puree); discard solids. Rinse out blender. Add raspberries and 1/2 cup each sugar and cream; blend until smooth. Pour through a clean sieve into another bowl, pressing on solids (you should have about 2 cups puree); discard solids.
Fill four 3-ounce ice-pop molds one-third full with blackberry puree and fill four molds one-third full with raspberry puree. Freeze until just frozen, about 1 hour. Pour another layer of purees, alternating them, over frozen layers to fill molds two-thirds full and insert ice-pop sticks. When second layer is just frozen, about 45 minutes, top with alternate purees and freeze until solid, 6 hours (or up to 2 weeks).