1) I have more than one digit.
2) Reversed number is subtracted to give at least 2 digit number which should be a cube.
2) you don’t even need a calculator to figure me out.
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The answer is
$41$. It is prime and
$41 - 14 = 27 = 3^3$
Assuming the number has 2 digits, it can be written as
$(10a + b) - (10b + a) = 9(a-b)$
should be a non-zero cube. The only way to make it a non-zero cube with single digits $a$ and $b$, is to have
$a = b + 3$
The only 2 digit prime number that fits is $41$.
As far as uniqueness of this solution goes, it is easy to show that no 3 digit number fits. I guess this is as far as you can go without a calculator :-)