1. Bring 1 cup water to a boil. Combine boiling water and tamarind pulp in a bowl; mash with a fork. Let stand 10 minutes. Mash tamarind again. Press through a sieve into a bowl, pressing pulp firmly against the sieve to extract all liquid. Discard solids.
2. Combine tamarind liquid and 1/2 cup water in a small saucepan over medium heat. Add sugar; bring to a boil, stirring until sugar dissolves. Reduce heat, and simmer 5 minutes or until liquid thickens slightly. Remove from heat; cool 5 minutes.
3. Combine tamarind syrup with remaining 6 cups water in a large pitcher. Serve over ice. Garnish with lime slices, if desired.
Note: Look for blocks of tamarind pulp in Asian markets; it keeps a long time in the fridge when well sealed. Avoid tamarind paste that's sold in tins or jars; it often has a metallic taste.