You shouldn't use $a as variable. $a and $b are special variables in perl, used to hold results from the sort function.

As stated by others, use the Data::Dumper module for printing hashes.

use Data::Dumper;
my %not_a_or_b=();

$not_a_or_b{1}{"a"}{"A"}="FIRST";
$not_a_or_b{1}{"c"}{"B"}="THIRD";
$not_a_or_b{1}{"b"}{"C"}="SECOND";

foreach my $k1 ( sort keys %not_a_or_b ) {
  foreach my $k2 ( sort keys %{$not_a_or_b{$k1}} ) {
    foreach my $k3 ( sort keys %{$not_a_or_b{$k1}{$k2}} ) {
     print "$not_a_or_b{$k1}{$k2}{$k3}\n";
    }
    
  }
}

print Dumper(\%not_aor_b);
[download]