Hi,
You have been given great solutions, but in the spirit of "tim today", you could also check this (a somewhat modifications to the solutions already given):

use strict;
use warnings;

my %logger;
my $key;
while(<DATA>){
    s/\s+$//;
    if(/\[(.*)\]/){
      $key = $1; 
    }else{push @{$logger{$key}}, $_;}
}
  
 print $_,":", join ("," => @{$logger{$_}}),$/ 
     for sort {$a cmp $b} keys %logger; 

__DATA__
[server1]
/tmp/location1/file.log
/tmp/location2/file.log
[server2]
/usr/loc1/file.log
/usr/loc2/file.log
[server3]
/citrix/dir3/file.log
[download]

NOTE:
Since, the key only changes, when the name of server is seen, and that until the next one. It works perfectly well.
You could also see perldsc