In a saucepan, bring 250 ml (1 cup) of the water to a boil with the sugar and cherries. Cover and simmer gently for about 10 minutes. Strain and discard the cherries. Let the syrup cool and refrigerate until completely chilled.
In a glass pitcher, place the tea bags in the remaining water. Place the pitcher outside or on the windowsill in the sun and let brew for 2 hours. Remove the tea bags and add the cherry syrup. Refrigerate. When ready to serve, add ice cubes.