Well, quite the stubborn tank you have. I will first say sorry if any of my suggestions are repeats of previous replies.
The first thing is do not clean the tank so much at the same time, all you are doing is repeating the cycle and the result will be the same, GREEN PEA SOUP! First, you must eliminate the source of nutrients that algae feeds off of. Assuming you have no live plants in the aquarium, Cover the tank in total darkness for about three to five days.
Feed the fish at night if you must, or better yet, if they are well fed, you can let them fast for a few days, it won't do them any harm. The idea is to eliminate two major nutrient sources, Ammonia and phosphates, especially phosphates. A product that I have recomended and use faithfully is a product called 'PHOS-ZORB'. It is made by Aquarium Pharmaceuticals Inc. Follow manufacturer's instructions and within a couple of weeks, you will see a dramatic change in your tank. It may seem pricey, but it is rechargeable many times over. The ammoina buildup in a tank is best kept down untill a healthy cycle is established, by using a bacterial culture additive. I prefer the liquid types. Remember, check the expiry date and refrigerate after opening. I initially use double the dose recomended for a new aquarium setup. This will also help reduce nitrates if there are high levels. Now, you are thinking, I do not want to wait two weeks, what then?
I can only recomend one thing in this case. A diatom filter, It will clean a tank from green to clear within minutes and the more you use it, the better it works. The only problem is you have not cured the problem, the diatom filter only effective if left as a permanent filter it can filter out particles as small as 3 microns, the human eye can see as small as 30 microns (approx.)
If you have objects with limestone, remove them, alkaline water is favorable to algae. Adding a peat extract or running aquarium grade peat moss in your filter will acidify your water. The tannic and hummic acids will stain the water, further reducing available light. Regular weekly water changes and carbon filtration will remove the staining over time. Most fish and plants do well in water that is slightly acidic.
Remember, do not do a water change and clean yor filter on the same day, give at least 72 hours in between those jobs. 20% of the total water volume should be changed per week that is in tanks 50 gallons or less. The slower you stock a tank with fish, the better. I take an average of a year to a year and a half to fully stock a tank, double that if it is a marine tank.
Leave as little organic material possible to decay in the tank. Aim for zero matter. If you see excess organic material, suck it up on the next water change and add bacterial culture.
Cheers,
Ick