So, why are you still getting nitrite readings then? If the tank is cycled, there should be none, if it isn't, that would explain it (just because you went through the motions of cycling, doesn't mean something hasn't killed off some of the bacteria since, and it is important to find out what it could have been).
What wattage are the bulbs, what diameter (T5, T8?) and how many do you have? Are the lights on a timer?
To solve the cyanobacteria problem in the long term, you need to solve the aforementioned nitrite problem and you should get a lot more plants, especially fast growing ones, as they will out-compete the bacteria.
So, first step I would take would be daily manual removal of all cyanobacteria until the nitrite problem is sorted. Once it is sorted, I would manually remove all the cyanobacteria that you can and do a 7 day blackout. On the day the blackout is finished, I would again manually remove all cyanobacteria and heavily plant the tank with suitable stem and floating plants, increasing lighting to 12 hours per day.
Basically, a tank your size can't sustain 4 swords without some serious fertilisation because they are very greedy plants and 6 hours of light per day, in my experience, encourages algae and cyanobacteria because that is not enough for the plants.
If a number of blackouts do not solve your problem, you may have to try antibiotics, to remove the last traces of it, but unless you solve the root cause, the bacteria will come back.
