Just because this solution hasn't been hinted at yet:

while (<DATA>) {
    chomp;
    if ( $. % 14 == 0 ) {
        print "$_ -- do something here\n";
    } else {
        print "$_\n";
    }
}
__DATA__
line 1
line 2
line 3
line 4
line 5
line 6
line 7
line 8
line 9
line 10
line 11
line 12
line 13
line 14
line 15
line 16
line 17
line 18
line 19
line 20
line 21
line 22
line 23
line 24
line 25
line 26
line 27
line 28
line 29
line 30
[download]

Don't forget this kind of solution will leave you with extra unprocessed lines whenever the total number of lines isn't a multiple of 14, so wrap those up after you're finished with the loop.