1) In a medium bowl, combine the gelatine and the sugar. In a small saucepan, bring water to a boil. Add boiling water to the bowl and whisk vigorously to dissolve the gelatine.
2) To the gelatine mixture, add 250ml of lychee syrup and rum and whisk again. Cut the lychees in half and place 1 half in each cup. Pour the gelatine mixture into the cups. Refrigerate until set.