Muddle mint in a pitcher or shaker. Add blueberry simple syrup, lemonade, and rum. Stir well, then add 7UP and gently stir. Pour into glasses filled with ice and garnish with mint and blueberries.
for the Blueberry Simple Syrup
Combine water, sugar, and blueberries in a small saucepan and bring to a boil over medium-high heat. Lower heat to a simmer and cook 5-10 minutes, until blueberries burst. Mash blueberries slightly with a spoon/masher to release more blueberry flavor.
Remove from heat and pour simple syrup through a fine mesh sieve, discarding solids. Let blueberry simple syrup cool completely and then refrigerate until ready to serve (up to a few days).
*you’ll have way more blueberry simple syrup than you need for 4 cocktails. Reserve extra syrup for more cocktails in your future!