In a large stock pot combine the apple cider, apple juice, sugars, cinnamon sticks and pumpkin pie spice. While stirring to dissolve sugars, bring to a light boil, reduce heat, cover and simmer for 30 minutes.
After 30 minutes remove from heat and let cool completely. When cool remove the cinnamon sticks and add the Everclear. Don't add the alcohol until completely cool or it will evaporate.