Halve the pomegranates and remove the seeds. Place the seeds in a pot. Cover the seeds with 1/2 liter (approximately 1/2 quart) of water. Add the sugar and simmer for 10 minutes. Pass the liquid throough a fine strainer and let cool.
Squeeze the mandarin oranges through a fine strainer into the pomegranate liquid. Before serving, add the ginger ale and the ice cubes. Garnish with the lemon balm, and serve.