Make the sugar syrup first by combining the Tate & Lyle Golden Caster Sugarand water together in a pan over a low heat. Stir to dissolve for 2-3 minutes then bring to the boil and boil for 1-2 minutes. Leave to cool.
Combine the raspberries and blackberries in a pestle and mortar and lightly crush them or put them in a small bowl and use the back of a wooden spoon instead.
Fill 4 tumblers with crushed ice, pour over the sugar syrup, then add the crushed fruits, followed by the lime juice and rum. Stir to combine, then decorate with a mint sprig and serve with lime wedges.
Make the sugar syrup up to one week ahead and store in a jar in the fridge.