Combine the sugar with 1 cup water in a small saucepan, and heat until the sugar dissolves completely. Set aside to cool or refrigerate for up to 2 weeks.
When ready to make the cocktails, combine the lime juice, 1 cup of the sugar syrup, and the rum in a pitcher. Fill 6 cocktail glasses with ice and pour the mixture over the ice. Garnish each cocktail with a slice of lime and serve ice cold.