Essjay is correct, using antibiotics (or other chemicals) is more dangerous than beneficial. She is also correct when she says you need to find the cause and deal with that. I can guarantee than any treatment, including blackout, will not benefit permanently without the actual source/cause being resolved.
Cyanobacteria is, as the name indicates, not an algae but a bacteria, which is why some suggest antibiotics but this is not the best option as they affect fish and the biological system in other ways. And cyanobacteria is caused by organics in the presence of light. The organic level is obviously high; this can be caused by too many or too large fish, overfeeding, over-fertilizing plants, insufficient filter cleanings, insufficient water changes (volume and/or frequency), insufficient substrate vacuuming, or sometimes (unfortunately) they just occur, but this is not as common as the obvious causes that can be rectified.
No mention is made in this thread of nitrates, but I would suspect they are probably higher than normal, or just high. Can you test nitrate and let us know? And if using the API liquid nitrate test, shake Regent #2 for a good 2 minutes (not just the 30 seconds) before adding the drops. Also, what is the pH?
Organics occur from having fish in the tank, obviously, but we need to reduce them. I have dealt with cyano twice, or maybe three times, in the same tank. I haven't seen it now for five or six years. I mentioned some causes of excess organics above, and therein lies the treatment. The best treatment is to remove as much as absolutely possible at one go, with a water change and deep substrate vacuuming; use your fingertips to remove it from objects including plant leaves and it will drop to the substrate where it can be siphoned out. If you fertilize for plants, stop it temporarily. Reduce fish feeding amounts if this seems a possible cause (you can not feed them for a few days). I personally would not do a blackout if you have live plants, as you want the plants to use the organics/nutrients more, and this requires light to drive photosynthesis. It took me three, maybe four weeks of this extra cleaning during the weekly water change to get rid of this, along with reducing light (I cut it back from 8 to 7 hours daily); each week it was increasing far less than before. Persistence and rectifying the causes is the only way to deal with this.
