Using an extra-large stockpot (I used a 12-quart stockpot), over high heat, add in the cored and quartered apples, oranges, cinnamon sticks, star anise, whole cloves, whole allspice, sugars, and water. Stir to mix.
Bring the mixture to a low boil, then reduce the temperature to medium-low, and let it simmer for 1 ½ hours. Stir the mixture occasionally.
After the apples and orange mixture has been cooking for 1 ½ hours, using a potato masher, carefully mash the apples and oranges to help release more of their juices. Continue to simmer for another 30 minutes.
Remove the stockpot from the heat. Carefully ladle the cider through a fine-mesh sieve to remove large pieces of apple skin, orange rind, and whole spices.
Once the cider has been filtered, you can return the cider to the stovetop to keep warm before you are ready to serve.