No real need for Perl references in my view, nor for any complex data structure. A simple array should do the work (if I understood the requirement well).

use strict;
use warnings;

my @sums;
$sums[$_] = 0 for 0..20;

while (<DATA>) {
    my @fields = split /\s+/, $_;
    for (0..20) {
        $sums[$_] += $fields[$_] if defined $fields[$_];
    }
}
print "@sums", "\n";

__DATA__
1    2    3    4    6
3    4    5    6
6    7    8    9
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My only assumption is that the number of columns is equal to or less than 21. This is the resuling outputt;

$ perl column_sum.pl
10 13 16 19 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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