I think one thing needs to be cleared up. The bacteria involved in denitrification do not use carbon as a food source, they use nitrogen. So they have nothing to do with this. I see at least two good explanations for what is happening. One is that the nitrates and sugar are forming a nitrogenous organic compound which is removed by the skimmer which is very plausible. Secondly, the sugar could be reducing the nitrates to nitrogen gas which is then expelled from the tank. There is some research on the use of sugar to reduce nitrate but not in water only in glass formation. These same explanations would hold true for the use of vodka also for those interested.
As for inorganic phosphates they can be removed by using a product called Phosbuster Pro, which is nothing more than ferrous chloride, or sulfate not sure which as it is not listed but both do the same thing, which flocs out the phosphates (inorganic only). It will initally turn your water cloudy as the floc forms, I use filtration to remove the floc. I personally have used Phosbuster to reduce my inorganic phosphate levels to near 0 from a high of 8 ppm. I now use a granular ferric hydroxide in a canister filter to keep the inorganic phosphates down and dose the Phosbuster about once a month. My organic phosphate levels are another issue, around 0.50 ppm and nothing seems to change them, even skimming. By the way Ferrous chloride has been used for decades in removing phosphates from wastewater by water treatment plants.
For the nay sayers out there I have 20 years experience in the water treatment industry and am an inorganic chemist by trade and a microbiologist by training. I have 40+ years FW tank experience and am just starting out with reefs. So give the kid who discovered this method a break as it is possible and I see no harm in adding sugar to a tank in small doses. 90% of the crap sold as additives don't even have a list of the ingredients and people happily pour the stuff in their tanks without a care.