How I calculate the cube root of large numbers by short tricks?

You need to find the cube root of X

Take any number (Y) and cube it.

* ....If it is smaller than X, add 2 to Y and cube thatnumber. Repeat that process until you get a cube which is larger than X. Subtract 1 from the last number you cubed and cube that number. This will give you either the exact X you were looking for, or a very close number. * .... If it is larger than X, subtract 2 and cube that number. Repeat until you get a cube which is smaller than X. Add 1 the last number you cubed and cube that number. This will give you either the exact X you were looking for, or a very close number.

If you get to "a very close number" then you are seeking a root which will be fractional, and you need to repeat the process above with decimal places.

* .... if the cube root of 'the very close number' is Z, add .5 to Z and cube that, and continue fine-tuning the decimal places until you get so close as to make little difference to the result.