Bring all ingredients to a boil in a large pot or dutch oven. Reduce heat to simmer. Cover and simmer 20 minutes, stirring a few times to make sure the blackberries cook down.
Remove from heat. Remove the cinnamon sticks and let sit for 5-10 minutes, or until cool enough to handle.
Strain through a fine mesh sieve or cheesecloth. Repeat if necessary.
Enjoy warm right away or refrigerate for a cold cider drink. Will keep in the fridge for up to 1 week.