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my $dim  = 3;
my @size = (4, 5, 6);
...
$str .= " = 0;\n";

$str .= "  " x ($dim - $_) . "}\n" for 1 .. $dim;

for my $a (0 .. 4 - 1) {
  for my $b (0 .. 5 - 1) {
...
    }
  }
}

  my $i = 0;
  my $sub = 'sub { $array' .
            join '' => map {'[$_[' . $i++ . ']]'} 1 .. $dim;
  $sub .= ' = $_[-1] }' . "\n";

sub { $array[$_[0]][$_[1]][$_[2]] = $_[-1] }