One of my projects for this year was to see if I could get some sugar from sugar beets. After sourcing some seeds online and growing a 6x3' bed, I ended up with a good sized pot after I topped, skinned and cubed them (took about an hour). In the picture below, the beets are just barely covered with water (wine bottle for scale--it was a lot of beets!).
According to the instructions I found, the way to do this at home is to boil them for about an hour, separate the sugar-filled beet water from the beets (which can then be used or composted) and boil the water down. Once you have concentrated the juice (another two hours of simmering), you let it sit and the sugar slowly crystallized out. I ended up with two quarts of concentrate.
The instructions were vague about whether refrigeration is necessary. My guess is yes as otherwise the sugar-water will start to ferment (making a nasty-tasting quasi-rum, I'm told). I did have a taste of the concentrate and it has a distinct beetish taste that I hope will be left behind when the sugar crystals form! All told, a nice project for the first snowy day of fall, but getting sugar from beehives has to be a lot easier!