Blackouts do not work permanently. Cyanobacteria is caused by high organics in the presence of light. The only way to get rid of it is by removing the organics (as much as possible) and ensuring organics remain under control. I have dealt with this a couple times over 12 years.
Light is important, but it is not the direct cause. What I did was reduce the tank light period by one hour (down to 7 hours from 8 at the time), clean the filter (all that brown/black gunk is organics), clean the filter tubes as best you can, do a major water change with a good vacuum of the substrate to remove more organics. Before doing the water change, manually remove as much of the cyano as you can from surfaces like plant leaves and wood/rock; it will float down and settle on the substrate so it is easier to vacuum out. It took me a few weeks to eliminate it completely, but every week it was less than the week before.
At the same time, reduce fish feeding, the prime source of organics. Feed only what the fish need, once a day, miss alternate days or similar. Obviously don't overstock the tank, the more fish or the larger the fish the more waste. I also found that reducing plant additives seemed to help, as these are another source of organics or perhaps the reduction in additives allowed the plants to more fully utilize the organics, whichever.
Antibiotics will obviously work, as this is a bacteria, but these should never be used in a tank with fish unless the antibiotic is specific to a fish disease and the best treatment. Any chemicals/medications intended to deal with cyano (or algae) should never be used with fish present. But the bottom line, no matter which treatment, if the cause of the organics is not rectified the cyano will come back.