Pour the vodka into a large, sterilised Kilner jar or similar container. Add the blackberries and the sugar, then seal tightly and give the jar a good shake. Leave in a cook, dark place for 3 days to allow the flavours to infuse, shaking daily.
Strain the berries and vodka through a fine sieve lined with a muslin or a new, clean, damp, J cloth. (it's important that the fine debris in the mixture is removed from the liquid, otherwise it will ferment and spoil the vodka.) You may have to do this a few times to remove all traces of the fruit.
Pour the vodka into sterlised bottles or jam jars and seal them securely. Keep chilled and consume within 8 weeks.