Put 2 cups of water in a saucepan and add the granulated sugar. Heat over low heat until the sugar has dissolved. Bring to a boil, then reduce the heat and simmer for 5 minutes. Set aside to cool, then stir in the fresh lemon juice.
Put the sugar syrup and mixed berries in a large food processor fitted with the metal blade and whizz for 20 seconds, or until smooth. Press the puree through a sieve in batches and pour into a wide, deep plastic container.
Freeze the mixture for 1 to 2 hours, or until ice crystals have formed around the edges.
Using an immersion blender (or regular blender), whizz the mixture to break up the ice crystals. Return to the freezer and repeat this process for 4 to 5 hours until the berry mixture resembles soft snow.
To Make the Raspberry Cream: Whizz the raspberries and confectioners' sugar in a food processor for 10 seconds, or until smooth. Press through a fine sieve. Lightly whip the cream until it just holds its shape. Fold the cream into the raspberry puree.
Serve the frozen sundae mixture in chilled glasses with a spoonful of raspberry cream and some fresh berries.