Another approach is to recognize that if you know a number is a perfect cube, and you can recognize any prime factors it contains, you can pull out the cube of

Another approach is to recognize that if you know a number is a perfect cube, and you can recognize any prime factors it contains, you can pull out the cube of those from the number. Like, by inspection (sum of digits) this number has 3 as a factor. That means 3 has to also be a prime factor of its cube root which means 27 has to be a factor of the cube. So we can divide out 27, leaving us with the smaller problem of finding 3(cbrt(729)), which you might recognize as being 3*9, or spot that you can repeat the trick to give you 9(cbrt(27))… Or you might notice that if 19683 has to contain 27 as a factor, that doesn’t leave a lot of room for any other cubed prime factors to exist in the number, and do a trial multiplication to confirm that 27 just is the cube root. Basically comes down to, if you have a comfortable relationship with how numbers relate to their factors, you can develop a number of instincts for how to recognize shapes within them.