while (length $input > 6){
   my $front = substr($input, 0, 6);
   $input    = substr($input, 6);
   push @sets_of_six, $front;
}
[download]

This can be done slightly more compactly by having the initial substr remove the leading characters as it retrieves them:

while (length $input > 6){
   my $front = substr($input, 0, 6, '');
   push @sets_of_six, $front;
}
[download]

(Or even get rid of $front entirely with

while (length $input > 6){
   push @sets_of_six, substr($input, 0, 6, '');
}
[download]

if you don't think that's becoming too unreadable.)