If a cubesat is launched as secondary payload to LEO, what ways are there to put it in a higher orbit, for example outside of the van Allen belt to make a radiation experiment? The ISS launches cubesats and larger minisats. Can it help a sat leave LEO?
An alternative is to launch from the ISS with a catapult (eg railgun/coilgun) or a small single stage solid rocket. This would give an elliptical orbit, so only part of the time would be spent at the target altitude.
(Note that at the moment the CubeSat Requirements Document prohibits propulsion systems on CubeSats though. Presumably this would include ion drive as well as the more obviously hazardous solid rockets. So launching self propelled cubes directly from the ISS is really only a theoretical possibility at the moment.)
As long as there are ways to change its velocity, the CubeSat can move to a higher orbit.
However, the CubeSat deployers onboard ISS are most likely spring-driven and will not provide much delta-V for the job. If they equip ISS with a railgun and somehow find a way to deal with the reaction, it will certainly launch a CubeSat to orbit higher than LEO.
Using ion thrusters on a CubeSat will probably be more easier than the a railgun method.
A common limitation on CubeSats is that they can't contain explosives or high-energy substances, like rocket fuel. But there is a project testing the use of water for fuel. In orbit, the water is hydrolyzed into hydrogen and oxygen with electricity generated by solar panels. So the fuel is completely inert when it is loaded on the rocket and traveling with other people's payloads, then prepared in situ. Another advantage is not having to store cryogenic fuels. No telling when this will come into practical use, but it seems like a pretty clever idea to me.