I did some experiment with a low power solder iron (15Watt)and plastic from a revenge. I filled the caps between the cubies of a 4x4x4. This might also work to build the wall cube. I use the solder iron to melt the plastic and fill the cap.

This is the result of the first try. I now will look if this method is usefull. At least it is very cheap!!

I used a spare part (of an other cube), melt it first and put it on top of the cap, You can use the solder iron to flat out and melt the plastic.

DO NOT melt the existing plastic!

Use only a LOW power Solder iron!!

This is a brilliant method! And you could do some extra sanding and buffing if needed.

I just tried Ton's method... it works great. Use ONLY a 15 watt soldering iron... i tried 20, it didnt work, i had to go buy a new one. Afterwards, i sanded it smoothe with a dremel.

On the puzzles I make I use Humbrol Model Filler.
I use it to fill minor 'gaps' in the pieces I adapt/construct/make for my transformations, and also to fill the larger 'gaps' that are created when sticking pieces together, as in Revenge pieces as described previously.
This is a paste like substance that comes in a tube, it has to dry (time depends on thickness - if a thickness is required it is best applied in layers). When it is hard it can be sanded to a perfectly smooth and pristine finish. Obviously the more time spent the better the result. Sometimes the time I spend on puzzles is incredible, but I beleive it is worth it.
Just a thought.

Is this available at any hobby store??

I get it from model shops, the kind that sell plastic kits etc..
If you can get it in England you should be able to get it anywhere.
Of course it may be under a different name. But I'm sure you'll be able to get an equivilent.
Good luck.