Combine all ingredients (except beef brisket, beet or sauerkraut juice and ice cubes) in a large stockpot.
Bring brine to a boil, stirring frequently.
When sugar and salt have dissolved into the water, remove the brine from heat and add the ice cubes to begin cooling the mixture.
Place the brine in the refrigerator for several hours (6-8 hours) to cool the mixture completely. The brine should be as cool as 60°F to 70°F before adding the meat.
Once the brine has cooled, add the beet or sauerkraut juice and stir to combine.
Place the beef brisket in a large baking dish or 8 quart bowl. Pour the brine over the beef, until it is submerged in the brine completely. Seal the container with a lid or plastic wrap.
Place the beef brisket in the refrigerator in the brine for 3-5 days. Be sure to flip the meat and stir the brine once each day.
After 3-5 days, remove the beef brisket from the brine and rinse in cool water. Cook corned beef as usual.