In a shaker, dissolve the sugar cubes in 1 ounce of the club soda.
Add the cardamom and muddle.
Add the rum, lime juice, grapefruit juice and bitters, one at a time, while stirring.
Fill with ice and stir.
Strain into a cocktail or punch glass and top with the remaining 2 ounces of club soda.
Garnish with lime wheels.