Place the sugar and water in a small saucepan and bring to a boil, stirring to dissolve the sugar. Add the basil leaves, cover, and remove from the heat. Let sit for 15 minutes, then strain and discard the basil leaves. Transfer syrup to a heatproof bowl and refrigerate until well chilled.
When the syrup has chilled, place the cubed mango in the bowl of a food processor or a blender and puree, adding the syrup little by little until it is fully incorporated and the fruit mixture is very smooth.
Divide the fruit puree among 6 or 8 (5-ounce) paper cups. (Alternatively, the mixture may be frozen in ice cube trays or in icepop molds, if available.)
Stand and ice-cream stick or plastic spoon in the center of each cup.
Cut 6 pieces of aluminum foil about 4-inches square. Poke a small hole in the center of each foil square and place 1 square over each cup, pushing the stick or spoon handle through the hole to hold it in a straight upright position.
Stand the cups in the freezer and freeze until set, at least 8 hours or overnight. Remove the pops from the freezer and discard the foil squares.
Gently tear the paper cups away from the fruit pops and serve.