MASH together blackberries and sugar in a medium bowl with a potato masher. Press mixture through a fine wire-mesh strainer into a small bowl, using back of a spoon to squeeze out juice. Discard pulp and seeds.
POUR blackberry mixture into a large pitcher. Stir in tequila and lemonade concentrate until blended. Stir in club soda and ice cubes. Serve immediately. Garnish, if desired.
Note: For fast measuring, you can use the empty can of limeade concentrate to measure the tequila. Half of a 12-oz. can is equivalent to 3/4 cup.