Place pieces of orange in each of 8 (12-ounce) rocks glasses, and top each glass with a couple basil leaves or a mint leaves. Sprinkle 2 teaspoons of cane sugar in each glass and, using a muddler, crush the orange pieces while bruising the basil with the sugar. Fill each glass just below the rim with ice (about 1 to 1 1/4 cups in each glass). Add a tablespoon of the basil syrup and 1/4 cup of the rum to each of the glasses.
Use a shaker to vigorously shake the contents of the glass together for at least 30 seconds. Pour the mojito back in the glass, and top off the glass with seltzer or sparkling water. Place a sugar cane stick in each glass. Garnish each drink with 1 of the remaining basil or mint leaves. Serve immediately.
Place the sugar and the water in a small saucepan. Bring to a gentle boil over medium-low heat, stirring occasionally to help dissolve the sugar. Once the sugar has dissolved, remove the syrup from the heat, and add the basil leaves to the saucepan. Allow the syrup to sit for at least 1 hour before straining through a fine-mesh sieve. Discard the basil leaves. Store the syrup in an airtight container and place in the refrigerator until ready to use. Syrup will keep, refrigerated, for several weeks.