Wow! That took me a couple of minutes and I used the binomial theorem... Can I ask, in what sense did your DS do it, and do you know how? There are three different things that come to mind, with different contexts for the question to occur:

- if he had started with the answer, cubed it, and then commented that [answer] is cube root of 12167, then this demonstrates formidable multiplication skills and a knowledge of what a cube root is;

- if you know the answer is a whole number, then you can work out which whole number it has to be using fairly basic techniques. (You can see what digit it has to end with, and then for the other digit you use Goldilocks.)

- if on the other hand you are answering "Is the answer a whole number, and if so, which?" then you have to be able to do both of the above things - or maybe you use some other method that isn't occurring to me!

I'd love to hear how he did it, or how he thinks he did it!
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