Don't Use A Calculator! 3

Apply the Squaring numbers ending in 5 trick from the Mental Math Tricks wiki, we have

$165^2= 100 \times 16 \times 17 + 25 = \large \color{#20A900}{\boxed{27225}}$

For squaring of numbers ending with 5, there is a simple technique.....
First write 25 at the end.
Then multiply the rest of the number excluding the 5, by its successor....(example: if $35^2$ then multiply 3 with 4)
write the product before 25...
here, 16 multiplied by 17 is 272 and then writing 25 at the end gives $\boxed{27225}$