Remember, an IP address is simply a 32-bit number. The dotted form is just a representation of that number. While the dotted form might be easier to transcribe, it's easier to work with the 32-bit number directly when working with subnets.

The following actually uses the packed form of the 32-bit numbers. It's easier to obtain, and allows for easy sorting (sort vs sort { $a <=> $b }).

use strict;
use warnings;

my $subnet_size = 29;
my $subnet_mask = pack('B*', ('1' x $subnet_size)
                           . ('0' x (32-$subnet_size)));

my @ip_xfers = (
   [ '10.0.0.1', 555555 ],
   [ '10.2.1.6', 444444 ],
   [ '10.6.2.8', 333333 ],
   [ '10.2.1.2', 222222 ],
);

my %subnet_xfers;
foreach (@ip_xfers) {
   my ($ip, $xfer) = @$_;
   my $packed_ip = pack('C4', split(/\./, $ip));
   my $subnet = $packed_ip & $subnet_mask;
   $subnet_xfers{$subnet} ||= 0;
   $subnet_xfers{$subnet} += $xfer;
}

foreach my $subnet (sort keys %subnet_xfers) {
   my $subnet_ip = join('.', unpack('C4', $subnet));
   my $xfer = $subnet_xfers{$subnet};
   print("$subnet_ip/$subnet_size: $xfer\n");
}
[download]

10.0.0.0/29: 555555
10.2.1.0/29: 666666
10.6.2.8/29: 333333
[download]

Since the OP was using NetAddr::IP, what follows is a version that uses that module.

I used the same approach as in my earlier post. The main difference is that sorting is trickier because we are working with the string form. A plain (lexical) sort won't do because 20.0.0.0 would sort after 198.162.0.0.

use strict;
use warnings;

use NetAddr::IP qw( );

my $subnet_mask = 29;

my @ip_xfers = (
   [ '10.0.0.1', 555555 ],
   [ '10.2.1.6', 444444 ],
   [ '10.6.2.8', 333333 ],
   [ '10.2.1.2', 222222 ],
);

my %subnet_xfers;
foreach (@ip_xfers) {
   my ($ip, $xfer) = @$_;
   my $subnet = NetAddr::IP->new($ip, $subnet_mask)->network();
   my $subnet_ip = $subnet->addr();

   # Save NetAddr::IP for sorting.
   $subnet_xfers{$subnet_ip} ||= [ $subnet, 0 ];
   $subnet_xfers{$subnet_ip}[1] += $xfer;
}

my @sorted_keys = sort { $subnet_xfers{$a}[0]->aton()
                                    cmp
                         $subnet_xfers{$b}[0]->aton() }
                  keys %subnet_xfers;

foreach (@sorted_keys) {
   my ($subnet, $xfer) = @{$subnet_xfers{$_}};
   print("$subnet: $xfer\n");
}
[download]

10.0.0.0/29: 555555
10.2.1.0/29: 666666
10.6.2.8/29: 333333
[download]

Update: I originally didn't sort the output due to the extra complexity.