I have no idea whether or not sugar is derived from potatoes on any commercial scale anywhere in the world in this modern era, but it was an intriguing idea in the early nineteenth century. Here is a brief description of the process from a book with the marvelously convoluted complete title of:
The Popular Encyclopedia: being a general dictionary of arts, sciences, literature, biography, history, and political economy, reprinted from the American edition of the 'Conversations lexicon' with dissertations on the rise and progress of literature by Sir D. K. Sandford, on the progress of science by Thomas Thomson, and on the progress of the fine arts, by Allan Cunningham (Glasgow, 1836)
The next useful product [after potato starch] derivable from the potato is sugar. The discovery by chemical analysis, that the potato, though far different in form, taste, and all external qualities, was perfectly similar in component parts to the different kinds of grain used for the food of the man, led naturally to inquiries, whether the products derived from these grains, by submitting them to different chemical operations, might not be procured also from this root. Complete success was the consequence. It was found, among other things, that a substance, possessing all the properties of sugar, though differing a little from that of the sugar cane, could be procured by a simple operation from the potato. Until lately, however, the discovery was considered only as a matter of curiosity, and was mentioned only among men of science. Experiments were tried, on an extensive scale, in the United States of America, to ascertain whether, in districts where the potato grows abundantly, this sugar might not be made advantageously both to the population of the district, and to the manufacturer himself. The potatoes were ground by a very ingenious and simple method, by exposing them through a box or hopper to the action of a wooden cylinder, having nailed upon it long strips of iron punched full of holes, to give them a rough grating surface. This cylinder was driven by a band of leather attached to the drum of a water-wheel. On filling the hopper with potatoes, and giving the grater the necessary motion, the potatoes were reduced with surprising rapidity to a fine pulp, from which, by the aid of a sieve and water, the starch, in great purity, was readily obtained. This apparatus ground 3500 bushels of potatoes without the least repair. The starch thus obtained was then dissolved completely in water, heated by steam let into it. A certain quantity of sulphuric acid, or vitriol, was then mixed with it, and heat being applied, the whole of the starch was converted into syrup. This was purified from the acid by adding quicklime, and then evaporated; when the result was an excellent sugar fit for all domestic purposes. A bushel of potatoes, weighing 60 lb., gives 8 lb. of pure dry starch; and from these 8 lb., 7 ½ lb. of sugar are obtained. This sugar ferments briskly, when made into beer, and yields a healthful and pleasant beverage. It will be of most use, however, for making sweetmeats, and may be used at table in place of honey, for which it is a good substitute. It has already become a great favourite with most persons who have become acquainted with it. Its taste is that of a delicious sweet, and as an article of diet it is probably more healthful, and less oppressive to the stomach, than an; other sweet substance in use. Potatoes are used extensively in the eastern part of Russia for making treacle, which is quite as sweet and good as that which we obtain from the tropics, but having less consistence.
There is more than one way to make sweet things with the potato of course. One can add sugar from other sources and make candy. I have previously given recipes for Tomato Marshmallows and Potato Fondant from a book called Candy-making revolutionized; confectionery from vegetables, written in 1912 by Mary Elizabeth Hall, but it has other potato sweets too.
Potato Caramel No. 1.
Stir well one pound of sugar, one cupful of milk, one cupful of Irish potato — boiled and sifted as directed before — two tablespoonfuls of butter and one-half teaspoonful of salt. Boil until thick, and thin with one-half cupful of milk, and again cook until thick; again thin with one-half cupful of milk and cook until the mass is of caramel consistency, tested in cold water. Stir as little as possible, but be careful that the mass does not stick to the bottom of the kettle. Pour on a well-oiled marble between candy bars. Dry two days, cut in strips and dry again before finally cutting in squares. Place them in a cold place for several hours and then wrap them in parchment paper. They keep well.
This is the kind of potato caramel that is especially good for chocolate coating, although all of the potato caramels can be chocolate coated. Make the caramels as above and allow them to dry in the open air for several hours and then cover with chocolate.
The process is fully as laborious as it sounds, but the results are more than worth the trouble. The repeated cookings give the characteristic caramel taste and color.
And from another source:
Potato Cocoanut Candy
1 medium sized potato
2 cups shredded cocoanut
2 cups sifted confectioners’ sugar
1 teaspoon vanilla
Cook potato in boiling water until soft, and force through a coarse sieve or a potato ricer. There should be half a cup of potato. To this add sugar, cocoanut, and vanilla, working together until well mixed. Press one inch thick into small bread pan, and spread top with a thin layer of melted bitter chocolate or sweet chocolate. When chocolate is firm, cut in small squares.
This can be varied by using nuts or fruits instead of cocoanut.
The Candy Cook Book (1918) by Alice Bradley