1. Place the sugar and water in the bowl fitted with the mixer. Launch at speed 4 at 210°F for 3 minutes.
2. Add orange, grapefruit and lemon juices. Mix at speed 7 for 30 seconds. Pour the mixture into two large ice cube trays and place in the freezer for at least 6 hours.
3. When the cubes are frozen, unmold 1 tray into the bowl fitted with the kneading/crushing blade. Loosen with table knife if necessary. Pulse for 30 seconds. Scrape down the sides of the bowl, then add 1 egg white and 1 Tbsp. powdered sugar. Mix at speed 10 for 15 seconds.
4. Repeat with the remaining cubes of mixture, egg white and powdered sugar. Serve immediately or place in the freezer a few more minutes for a firmer texture.