Can the base M number 2009 be a perfect cube, where M is a positive integer ≥ 2?

If the answer is yes, give an example. Otherwise prove that the base M number 2009 can never be a perfect cube.

(In reply to analytic solution by Daniel)

Daniel, why do you restricted your (well done) analysis to base 9? In fact, as pointed out by Sing4, base 9 is the most unlikely base (since we have the digit 9 in 2009).

What am I missing? 

Posted by pcbouhid on 2009-03-10 09:00:11