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