Bring a large pot of water to a boil and cook the unpeeled beets just until fork-tender. Immerse in a sink of cold water, then remove the skins.
Slice beets about 1/4 inch thick, and pack snuggly into to the jars, taking care not to bruise or crush them.
In a large saucepan combine the sugar, water, vinegar, ground and whole cloves, allspice, and 1 whole cinnamon stick. Bring to a boil, then reduce heat and simmer for about 10 minutes.
Add one third cinnamon stick to each jar then pour the brine over the beets, leaving 3/4 inch headroom between the brine surface and rim of the jar. Wipe rims and threads clean with a damp cloth, then add the lids and bands.
Add jars to a water bath canner, bring to a boil and process in a boiling water for 12 minutes.
Cool on a rack, then label and date. Store in a cool, dark, dry cupboard.