Generally frameworks do not have user interface. If you have an UI, you need to test the UI also, and it makes some of the functionality testing easier.
Framework usually expose a set of API's. So testing a framework invloves a lot of white box testing.
What you can do is
1. Call the API's with a set of parameters and verify the expected result and say the test case has passed or failed.
2. Call the API's for many possible combinations of parameters and verify the result.
3. Call the API's and verify the database changes(by querying the database)
>it is also recommended that to test a new framework, build a demo application that is using all features of framework
Yes, it is. Still it has nothing to do with colour of the box. You could test this way either documented features or cover code of the framework. So do you want to know how to test (approach) or what to test for (coverage)?