Halve 2 limes and 4 mandarins and squeeze them. Wash the remaining limes and mandarins in hot water, dry them and chop them finely. Wash mint, shake dry and pluck off leaves. Spread the lime and tangerine cubes on the glasses.
Spread the sugar evenly on top. Crush a little with a wooden spoon handle. Fill glasses full to the brim with ice. Pour rum over them.