... as far as I am aware I cannot define side-effects for a subroutine in Perl....

It's easy:

use 5.010;

sub square_a_number
{
    my $value = shift;
    $Some::Global::Variable += $value;
    say "Squaring the value '$value'";
    return $value * $value;
}
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There are two trivial side effects, as well as the non-obvious side-effect of setting SvNOK on $value.