Wrap beet in aluminum foil and place in a 350-degree oven for 1 hour.
Let cool and peel off skin. Dice into ¼” squares (this should yield about 1 cup of roasted beets).
Place beets in an airtight container with the cane sugar, stir to incorporate.
Let rest on the counter or in the refrigerator for 2-3 days, stirring daily.
Strain into a new container, and then pour the vinegar through the beet mixture into the same new container.
Stir to incorporate, and chill to use in cocktails.