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.