Adding up the values in a hash (Perl)

To use the sum function, you need the List::Util package. But that isn't needed in this case, as you can use the + operator:

$value_count = $value_count + $words{$key};
# or $value_count += $words{$key};

In fact, you could use sum and avoid the loop. This is the solution you should use:

use List::Util 'sum';
my $value_count = sum values %words;

The values function returns the values of a hash as a list, and sum sums that list. If you don't want to sum over all keys, use a hash slice:

use List::Util 'sum';
my $value_count = sum @words{@keys};

You should be fine if you replace:

$value_count = sum($words{key}, $value_count);

With:

$value_count += $words{key};