In the bottom of a highball glass, combine the sugar, lime pieces, and blackberries and gently muddle well to allow the blackberries and lime pieces to release their juices. Add the basil leaves and mint and gentle muddle to allow their flavours to release.
Add the white rum and ice and stir well to combine. Top with soda water and garnish with some whole blackberries, a bit of basil, and some mint.
If you want to make a big batch, just assemble the mojitos in a pitcher!