Create an array in the output format you want and sort that.

#!/usr/bin/perl
use strict;

my $free_space = {
  node3   => { cores => 11, mem => 200 },
  node10  => { cores => 10, mem => 900 },
  node12  => { cores => 11, mem => 500 },
  node23  => { cores => 12, mem => 350 },
  node456 => { cores => 12, mem => 400 },
  node534 => { cores => 12, mem => 400 }, 
};

my @CoreMemNodes=();
for (keys %$free_space){
  my $hr = $free_space->{$_};
  push @CoreMemNodes,[$hr->{'cores'},$hr->{'mem'},$_];
};

my @sorted = sort {$b->[0] <=> $a->[0] 
                || $b->[1] <=> $a->[1]
                || $a->[2] cmp $b->[2] } @CoreMemNodes;

print "@$_\n" for @sorted;
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poj