Step 1

To make ice block, fill carton with water and freeze until solid, about 8 hours (see cooks' note, below).

Step 2

Stir together sugar and 31/2 cups water in a large bowl or pot until sugar is dissolved. Add lemon juice, rum, Cognac, and brandy and chill, covered, at least 3 hours.

Step 3

Put ice block in a punch bowl and pour punch over it.