use warnings;
use strict;

my $data = do { open my $fh, '<', 'sample.txt' or die $!;
	local $/; <$fh> };  # slurp whole file into memory

my $regex = qr{ 
	^ \s*APP>\sSTART_PARTU_8X8 \n
	^ \s*APP>\sPARTITION_SPLIT \n
	(.*?)
	^ \s*APP>\sEND_PARTU_8X8 $
	}msx;

if ($data=~$regex) {
	print $1;
}

##</code><code>##

use warnings;
use strict;

my $beg1 = qr/^\s*APP>\sSTART_PARTU_8X8$/;
my $beg2 = qr/^\s*APP>\sPARTITION_SPLIT$/;
my $end  = qr/^\s*APP>\sEND_PARTU_8X8$/;

open my $fh, '<', 'sample.txt' or die $!;
my $prev_line;
my $state = 'not_in_block';
while ( my $line = <$fh> ) {
	if ( $state eq 'not_in_block' ) {
		if ( $prev_line && $prev_line=~$beg1 && $line=~$beg2 ) {
			$state = 'am_in_block';
		}
	}
	elsif ( $state eq 'am_in_block' ) {
		if ( $line=~$end ) {
			$state = 'not_in_block';
		}
		else {
			print $line;
		}
	}
} continue { $prev_line = $line }
close $fh;

##</code><code>##

    START_PARTU_4X4
    ........
    START_PARTU_4X4
    ........
    START_PARTU_4X4
    ........
    START_PARTU_4X4
    ........