What is the correct usage?
- 10 × 10″
- 10″ × 10″
That is, is the double prime supposed to be on the first number or is it assumed to be the same as the second number when conveying measurements in inches?
Almost all of 800 written instances of 4 by 4 posts in Google Books will reflect OP's context.
If you glance through them you'll see that although most don't have any "double primes", those that do always seem to include it on both measurements.
In this respect the written convention doesn't precisely reflect spoken usage, where it wouldn't be particularly unusual to ask for a Four by four inch post.