First to make the cucumber syrup, bring the sugar and water to a boil in a small pot. Reduce the heat and stir until the sugar dissolves. Remove the sugar water from heat and stir in the grated cucumber and muddle the cucumber. Let it cool. Pour through a strainer into a bowl or measuring cup, and discard solids (you should have 2 cups cucumber syrup). Your cucumber syrup can be refrigerated up to 3 days.
Combine the cucumber syrup, Indiana Vodka, cranberry, and lime juices in a 2-quart pitcher. Serve over ice, and garnish with cucumber wedges. Your pitcher will remain fresh for about 8 hours.