Combine tamarind, dates, and 2 1/2 quarts water in a medium pot and bring to a boil; simmer briskly, stirring often and mashing pulp and dates with the back of a spoon until they break down, about 15 minutes.
Remove from heat and let steep for 2 hours.
Strain mixture through a fine-mesh sieve into a large bowl, pressing on solids to extract as much liquid as possible (you should have about 4 cups).
Transfer tamarind mixture to a pitcher. Stir in sugar and 3 cups water. Chill until cold.
Fill glasses with ice. Divide agua fresca among glasses.
