In a blender, combine the watermelon cubes and cucumber slices. Blend until smooth.

Strain the mixture through a fine mesh sieve into a large pitcher to remove pulp, pressing down with a spoon to extract as much juice as possible.

Add the fresh mint leaves and lime juice to the pitcher. If you prefer a sweeter drink, stir in the agave syrup.

Fill glasses with ice cubes and pour the cucumber-melon mixture over the ice, filling each glass about two-thirds full.

Top each glass with soda water or sparkling water and gently stir to combine.

Garnish with additional mint leaves or cucumber slices if desired. Serve immediately.