Special equipment: cheesecloth
Peel the cucumbers, saving the peels. Grate cucumber flesh on a box grater. In a medium saucepan, bring sugar and water to a boil. When sugar dissolves, add the grated cucumber and simmer until cucumber is tender, about 10 minutes. Remove from heat and let cool slightly.
In a blender, puree reserved cucumber peel and cucumber syrup until smooth. Line a strainer with cheese cloth over a bowl. Strain cucumber mixture. Gather cheesecloth in 1 hand to squeeze out all of the juice. Chill until cool, about 1 hour. Serve in glasses over ice.