Technically it should support up to the highest end iCore (a i7). The problem is that would no longer make this a "hewlett packard (model) 500-281" but a different model computer which would potentially violate your Windows license. The Windows license is TIED to the hardware, which means you can't modify the motherboard, cpu and sometimes not even replace the case itself (EMachines did this to me) without Windows ceasing working immediately when it starts up because it detects the difference so it know 'how to talk right to the hardware'.
Secondly to that, changing CPUs only helps if you need more 'processing', so if you multitask ALOT, with normally 30 windows open in Chrome, streaming both a video and music in two different windows, etc. all at the same time then it would certainly max out the potential for the i3. If your talking GAMING then even if you change the CPU the GPU will be a issue (and you already know the RAM isn't sufficient, and I hope your NOT running 32Bit Windows!!!) anyway.
Basically this computer is ONLY good for general school / PC use, not much more then that, as intended. If you want to upgrade to a more powerful machine, doing it piece meal off this will add a significant amount of costs that may be MORE then just buying a 'rig' specifically focused for your needs (best CPU available costs over $550 alone
http://pcpartpicker.com/part/intel-cpu-bx80648i75930k which is more then your PC cost I would bet!).
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