No because a^3 is not relative to b^3 or c^3 here because the depth of the cylinders is the same for all 3 and not just relative to a b or c
You have to think of it as a(b or c)^2 with a depth of (example) 3cm each

You just stumbled, completely by accident, onto one of the biggest stories in recent mathematical history. If you care enough google "fermats last theorem" and check out the wiki page.

I see this is quite interesting as most people would assume it could be done somehow
Has someone really tried this with every number combination possible?

No, that would be impossible as numbers don't have an end, i.e. if you give me a number I can always give a bigger one.
But number theory proofs tend to be iterative rather than exhaustive i.e. if we can prove it works for 1 then prove it works for n+1 then it must work for 1+1 and thus as it works for 2 also works for 2+1 etc etc.
If you're really interested there's a book called "Fermat's Last Theorem" by Simon Singh that doesn't require any mathematical knowledge to understand as it's more of a biography of Andrew Wiles life when he was working on the proof and a bit of history thrown in.
I'm a Math student at Uni and to me a problem that nobody could solve from 1637 till 1995 fascinates me.

Yeah I suppose so but wasn't the largest number supposed to be grahams number or something but i never got it because you could just add anything to grahams number

grahams number is the largest number with a use, it is very large, there are less particles in the known universe but it broke the record for largest number when it was used for a proof in some part of ramsey theory I think... not 100% on that but I bet Wiki would know =)

i was just putting it in those terms because volume is normally measured in cubic length

You do realize that those are the same thing right?

can't even begin to explain how wrong you are