try this:

use warnings;
use strict;

while(<ARGV>){
   chomp;
   print $1,$/ if/^sub\s+?(.+?){/; ## print subroutine name
   if(/^sub\s+?/.. /^}/){          
      print $_,$/;
    }
}
[download]

it works for me.
UPDATE:
The code above, is based on the assumption that:

1. the OP's script(s) start every sub on a new line,
2. the OP's script(s) and question does not cover anonymous subroutine

However, if these are not so, then all that is needed is to modify the REs used like so:

    ...
    chomp;
    print $1, $/ if /^(?:.+)?\bsub\s+?(.+?){/; ## assumption still her
+e
    if ( /^(.+)?\bsub\s+?(.+?)?{/s .. /^(.+)?}/s ) {  ## anonymous sub
+ included
        print $_, $/;
    }
   ...
[download]

Please, it should also be noted that the above may not take care of all subroutrine declaration in perl script.
rovf thanks for the eagle eye ::)