As others have pointed out already there's no sub inside a sub in your code. I'll answer the question asked in your title though:

I consider it a bad idea to define a named sub within another sub. It's visible from the outside still, but obeys rather unintuitive scoping rules:

 use strict;
use warnings;

sub a {
    my $x = 3;
    sub b {
        print $x, $/;
    }
}

b();
__END__
Variable "$x" will not stay shared at foo.pl line 7.
Use of uninitialized value $x in print at foo.pl line 7.
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There's no sane way in which perl could handle a call to b() from the outside.

However there's nothing wrong with defining an anonymous subroutine inside another sub. Actually it's quite common, and used very often in functional programming.