I'm sorry, but if it's a tank with the most basic of filtration, then it
is cycled properly.
A 20% water change will do very little to change high nitrates. With them being so high, I strongly recommend you test the change water before it goes into the tank. I also recommend that you are sure to be using a good quality test kit, like SeaChem or
Salifert.
If you don't use a protein skimmer, please get on. AquaC Remora and CPR BakPak are two popular brands, also do a search here
http://www.reefs.org/library and here
http://www.wetwebmedia.com
Also, if the problem isn't with the new water either, you clearly have nutrient export problems, ultimately with the nitrates. This is where a refugium and/or a deep sand bed (DSB) can work wonders. These two methodologies culture the anaerobic bacteria that break nitrogenous wastes (specifically your nitrates) down into more basic components.
First, do a couple of 50% water changes, and assuming that the new water doesn't reintroduce nitrates and you're using a good test kit, you
should see a small drop in levels, maybe from 200ppm to around 150ppm, if you're lucky even 100ppm (though don't expect that much of a drop).