I believe that whether you can run 64-bit guests on top of a 64-bit host depends on features of the CPU and BIOS.
However, you might try this first. Use "sudo apt-get purge virtualbox*" to remove any existing repository versions. Next visit https://www.virtualbox.org/wiki/Linux_Downloads and follow the instructions for "Debian-based" systems. Even though it does not appear in the list, on a 13.04 machine you should add the line
to /etc/apt/sources.list. Follow the instructions to download and install Oracle's public key, then use apt-get to install VB as described on the Downloads page. This method ensures that your installation of VB will be kept up-to-date automatically using the same system Ubuntu uses to update all the other software on your system.
deb http://download.virtualbox.org/virtualbox/debian raring contrib