You want the Schwartzian Transform. It looks to me like you want to sort the hash references by the sums of their values. (If I'm incorrect, you still probably want the Transform. You just won't be able to use my code. :)

my @hashes = (
    { key1 => 1, key2 => 4 },
    { key3 => 8, key4 => 4, key5 => 6 },
    { key6 => 3 },
);

sub sum {
    my $sum;
    $sum += $_ for (@_);
    return $sum;
}

@hashes = map { $_->[0] }
    sort { $a->[1] <=> $b->[1] }
    map { [ $_, sum( values %$_) ] } @hashes;

use Data::Dumper;
print Dumper(\@hashes);
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It takes a bit of thought to figure it out, but once you do, you'll have scary Perl kung-fu. The trick is adding extra data, sorting on that extra data, then discarding the extra data.