You can install 64bit version but if you don't want do this you can use PAE (Physical Address Extension) enabled kernel in 32-bit version.
After 10.04, ubuntu automatically installs the PAE enabled kernel if it detects more than 3 Gb of memory.But ubuntu wiki says:
In the case of the liveCD, a working network connection is required, since the PAE enabled kernel packages are not present on the CD.
So I guess you had installed ubuntu using CD without internet connection.
sudo apt-get install linux-generic-pae linux-headers-generic-pae
What is PAE?
Physical Address Extension is a technology which allows 32 bit operating systems to use up to 64 Gb of memory (RAM), something which is normally achieved by switching to a 64 bit system. PAE is supported on the majority of computers today and it is an easy procedure to enable it in Ubuntu, if it is not already. To check if your processor supports PAE, try
grep --color=always -i PAE /proc/cpuinfo
In general, a proper 64 bit system is recommended if you have 4 Gb or more memory and/or want to get the full benefit of the 64 bit architecture (see 32bit_and_64bit), but in some cases making a complete switch to 64 bit is not desirable, and using PAE can be a viable compromise.
It should be noted that there is no Virtual Address Extension. i.e. The applications still get the same amount of virtual memory since the Virtual addresses are still 32 bits while the Physical Addresses are of 36 bits. Therefore PAE is not at all equivalent to a 64 bit system.