In a small pot, bring water, sugar, and 6 cinnamon sticks to a boil. Reduce to a simmer and cook 8 minutes. Let cool to room temperature; discard cinnamon. (Refrigerate in airtight container, up to 1 month.) In a punch bowl, stir together cinnamon syrup, pineapple juice, rum, and lime juice. To serve, add ice and cinnamon sticks.
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