I'd like not to cheat if possible, but there has to be some sniff of logic the the puzzles.
If you cheat you will get caught and you will get chucked out, with no option to return ever again. Quite rightly so. The tests are not perfect but they are there for a reason. If you have to cheat, you are not suitable for the job.
There is logic to the puzzles, that is why they are included...
You have not applied yet, so if you are worried about the cubes, why not get some paper and scissors and cut yourself out all the different shapes that can be folded into cubes, then practice?
If you can't be bothered to do that when it seems that you do have a doubt about your spatial reasoning then, again, you are probably not suitable for the job.
Beware of what you write on PPRuNe - lots of people in the business read it - even the Chief Exec of NATS... there aren't going to be that many 'Adams' from Farnborough that apply to join NATS within the next couple of years... there are many traits within ATC, but mention of cheating is not a trait that will be welcomed by any of your future interviewers or instructors!