Place rhubarb into a large pot with the sugar and 1 quart of water. Bring to a boil, then simmer over low heat for about 4 hours, stirring occasionally to prevent burning, until rhubarb becomes a thick paste. Cool, then spoon into ice cube trays and freeze overnight.
Bring 1 quart of water to a boil. Pour into a pitcher over the tea bags. Stir in honey and sugar. Cool, then refrigerate until chilled. Serve cold ice tea with rhubarb ice cubes.