Try changing your foreach loop to a while loop. The effect of that will be to read the file line-by-line instead of attempting to load the whole thing into memory before processing it.

Well yes for a start you might strongly consider changing

foreach my $line (<DATASOURCE>){
[download]

while(my $line = <DATASOURCE>) {
[download]

/J\

Use a while loop rather than a foreach loop. foreach will read the entire file before anything happens because it provides a list context to the diamond operator (<DATASOURCE>). And you can let perl keep track of the line number for you because it's in the special variable $.:

#!/usr/bin/perl
use strict;
use warnings;

my $datasource ="C:\\somelargetextfile.txt";
open DATASOURCE, "$datasource" or die "Can't open $datasource: $!";
while (my $line = <DATASOURCE>){
   print "$. - $line";
}
close (DATASOURCE);
[download]

If this is all that your code is doing then I assume you're running on Windows because if you were on a unix, you could just use the cat(1) command to do something similar:

cat -n my_large_text_file.txt
[download]

Update: Ah, I see from your other post that you're inserting info into a database. Other than not reading the entire file into memory there isn't much else that you're going to be able to do to speed up the loop.

Why do you care how fast this program runs? Will it be run often? Must it finish within some time constraint so that it won't hold up a larger process?

use strict;

open my $hndl, '<'."bigfile.txt" or die "Open of bigfile failed $!";
while (<$hndl>) {
   print sprintf("%  7s",$.) . "  $_ \n";
}

close $hndl;
[download]

Off-topic from the original question, but whenever you do print sprintf, you should think about just using printf directly. I think this is clearer:

while (<$hndl>) {
    printf "%7d  %s\n", $., $_;
}
[download]