In a large stainless steel saucepan, combine apple cider and maple syrup.

Place cinnamon sticks, cloves, allspice berries, orange peel, and lemon peel in the center of a square of washed cheesecloth. Fold up the sides of the cheesecloth to enclose the bundle and tie it up with kitchen string.

Drop the spice bundle into the cider mixture.

Over moderate heat, cook the cider until it is very hot but not boiling, about 5 to 10 minutes.

Remove the cider from the heat and discard the spice bundle.

Ladle the hot apple cider into cups or mugs, and add a fresh cinnamon stick to each serving if desired. Enjoy!