If you are interested in using an XML parser instead of a regex, XML::Twig can give you the whole element you are looking for:

use warnings;
use strict;
use XML::Twig;

my $str = '
<DataEnd>
<Dataentry>
    <Data>aaaaaa</Data>
    <Data>aaaaaa</Data>
    <Data>aaaaaa</Data>
</Dataentry>
<Dataentry>
    <Data>aaaaaa</Data>
    <Data>aaaaaa</Data>
    <Data>aaaaaa</Data>
</Dataentry>
<Dataentry>
    <Data>aaaaaa</Data>
    <Data>bbbbbb</Data>
    <Data>aaaaaa</Data>
</Dataentry>
<Dataentry>
    <Data>aaaaaa</Data>
    <Data>aaaaaa</Data>
    <Data>aaaaaa</Data>
</Dataentry>
</DataEnd>
';

my $t = XML::Twig->new(
    twig_handlers => { Dataentry => \&dentry }
);
$t->parse($str);

sub dentry {
    my ($t, $ent) = @_;
    my $found = 0;
    for my $data ($ent->children('Data')) {
        if ($data->text() eq 'bbbbbb') {
            $found = 1;
            next;
        }
    }
    if ($found) {
        # do something
    }
}
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