Looking at the JVM versions posted as a minimum version is a good rule-of-thumb - you certainly want to avoid using anything lower. However, note that Cisco may not test any/all CUCM/JTAPI versions against JVM versions later than the documented version; while later versions will likely work (especially something close like Java8), there is a small possibility that if you encounter an issue in production, and Cisco support believes the issue is due to the JVM version mismatching, then they may not be able to troubleshoot/fix until a supported version is in place. This is mostly a theoretical concern, but for absolutely best results, assurance and supportability, using the documented version is recommended.
Note: we do have an inquiry into the JVM versions supported for CUCM 14, which should be added shortly.
