Peel the beets and cut into chunks. Place in a large saucepan with 6 cups water. Bring to a boil, reduce temperature and simmer until the beets are tender, about 20 minutes. Remove the beets from the liquid with a slotted spoon and reserve for another use. Bring the beet liquid back to a boil and let boil until reduced to 1 cup; about 25 minutes. Remove from heat, stir in the agave and let cool.