c:\@Work\Perl>perl -wMstrict -le
"my $s = qq{[20150302 22:01:05] [1, 2, 3, 4] String0\n [20150302 22:01:05] [1, 2, 3, 4] String1\n};
 print qq{<<<$s>>>};
 ;;
 my $t_stamp   = qr{ \d{8} [ ] \d\d (?: :\d\d){2} }xms;
 my $timestamp = qr{ \[ $t_stamp \] }xms;
 ;;
 $s =~ s{ $timestamp \s* }{}xmsg;
 print qq{<<<$s>>>};
"
<<<[20150302 22:01:05] [1, 2, 3, 4] String0
 [20150302 22:01:05] [1, 2, 3, 4] String1
>>>
<<<[1, 2, 3, 4] String0
 [1, 2, 3, 4] String1
>>>