Pull the leaves off of 10 sprigs of mint. Divide them among the 12 cups of a 12-cup muffin tin. Pour water over to cover. Freeze until firm, about 4 hours.
Combine the sugar with 1 cup water in a medium saucepan over medium-high heat. Bring to a boil and stir to dissolve the sugar. Add the remaining 10 sprigs of mint. Remove from heat and steep 15 minutes. Strain and allow the simple syrup to cool slightly.
Mix the gin, grapefruit juice, rum, tequila, triple sec, vodka and mint syrup in gallon-size container. Chill until ready to serve. Pour the mixture into a large punch bowl.
Pour in the cola just before serving. Float 6 to 8 grapefruit slices in the punch. Unmold the mint ice cubes and add to the punch bowl. Serve in cups over ice and garnish with mint sprigs.
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