Bring cinnamon sticks, cloves, ginger, water, and sugar to a boil in a small heavy saucepan, stirring until sugar has dissolved, then simmer, covered, 5 minutes. Remove from heat and let steep, uncovered, 1 hour.
Strain through a fine-mesh sieve into a bowl, discarding solids, then chill until cold.
Combine all remaining ingredients, except ice, with syrup in a punch bowl. Add ice before serving.
Cooks' notes: •To make hand-shaped ice, fill powder-free, latex-free rubber gloves with water and tie wrist end securely, then freeze.
•Syrup can be made 1 week ahead and chilled with spices. Strain before using.
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