To setup partition encryption on Ubuntu, perform the following steps:

Install the required software

apt-get install cryptsetup

For more security, erase the partition you want to encrypt with one of the following commands

sudo dd if=/dev/zero of=/dev/sdXN bs=4K
or
sudo badblocks -c 10240 -s -w -t random -v /dev/sdXN
or
sudo dd if=/dev/urandom of=/dev/sdXN bs=4K

Load the encryption kernel modules

sudo modprobe dm-crypt
sudo modprobe sha256
sudo modprobe aes

Enable encryption on the partition you want to encrypt

cryptsetup --verify-passphrase luksFormat /dev/sdXN -c aes -s 256 -h sha256

Map the partition you want to encrypt

cryptsetup luksOpen /dev/sdXN securebackup

Format the partition

mkfs -t ext3 -m 0 -O dir_index,filetype,sparse_super /dev/mapper/securebackup