Pour the apple cider and maple syrup into a large stainless steel saucepan.
Place the cinnamon sticks, cloves, allspice berries, orange peel, and lemon peel in the center of a washed square of cheesecloth; fold up the sides of the cheesecloth to enclose the bundle, then tie it up with a length of kitchen string.
Drop the spice bundle into the cider mixture.
Place the saucepan over moderate heat for 5 to 10 minutes, or until the cider is very hot but not boiling.
Remove the cider from the heat.
Discard the spice bundle.
Ladle the cider into big cups or mugs, adding a fresh cinnamon stick to each serving if desired.