Peel the 6 oranges, 6 limes, and pink grapefruit, removing the white skin. You can cut out the segments between the separating membranes, or slice and halve or quarter the pieces.
In a bowl, mix the cachaça and brown sugar together, stirring until the sugar dissolves completely, about 1-2 minutes.
Pour the cachaça mixture over the prepared fruit. Cover and refrigerate for at least 2 hours.
Spoon the fruit and marinade into cocktail glasses. Garnish each glass with a slice of orange or lime on the rim and top with lemon balm.