Well there are great threads about Cyano in here from the past...I know cause I was in them asking questions =)...
I've been through the really really bad outbreaks... and the main "source" is DOC's being high. You will get false readings on Nitrates to because the cyano is feeding on it ... for example your 20ppm reading may be actually higher but the cyano is eating it up.
Chemiclean is a very good product and many many folks use it for small outbreaks. Yours seems a bit much and it wont be solved by Chemiclean alone...if its as bad as I think.
Step 1 is to suck out every stinking piece you see.... if its on your sandbed ..definetly suck it off the sand and even the top layer of sand with it (it can reside below the top layer for later seeding)..
Step 2 do a very large water change...just punch that nitrite,nitrate,phosphate in the mouth with a good large water change.
Step 3. Add chemiclean wait the required time on the instructions and do another 20% change out of water (let it run its course).
After you do all that....you still have to identify "Why" it happened.
1. overfeeding is the main problem
2. bulbs going bad begin to change the uv spectrum that actually encourages its growth.
3. poor tank maintenance
I have the same cube. I've never had to deal with cyano in it. I dont even have power heads. Or a protein skimmer.
The question falls back to you now:
How often/and what do you do for tank maintenance?
Live stock quanity and how do you feed them..what do you feed...how often?
I've been through the most nasty Cyano break outs ever on my 55 gallon... I know that doing the cleaning steps above I finally put the halt on it.
Keyword search for old threads for Redslime... you will find a lot of information.
Remember you can clean all you like...but it wont stop it from comming back later till you identify the source of the issue. Chemiclean is just a temp fix...it wont remove the source per say.
I cant find the article I like the most but this one covers the basics:
http://www.aquariumpros.com/articles/algae.shtml Understanding our enemy the Cyanobacteria =)