Open up a terminal window [ Applications / Accessories ] and type the
following then press [Enter]

uname -a

If you see x86_64 in the output line then you have the 64bit version,
however the version you get depends on which ISO you downloaded to
create the installation CD. The default 'download' button on the
Ubuntu site would have got you the 32bit one - you have to select the
64bit version from a drop-down list.