It known that in C++ mocking/faking nonvirtual methods for testing is hard. For example, cookbook of googlemock has two suggestion - both mean to modify original source code
Code has to be written to be testable, by whatever test techniques you use. If you want to test using mocks, that means some form of dependency injection.
Non-virtual calls with no dependence on a template parameter pose the same problem as final and static methods in Java[*] - the code under test has explicitly said, "I want to call this code, not some unknown bit of code that's dependent in some way on an argument". You, the tester, want it to call different code under test from what it normally calls. If you can't change the code under test then you, the tester, will lose that argument. You might as well ask how to introduce a test version of line 4 of a 10-line function without changing the code under test.
If the class to be mocked is in a different TU from the class under test, you can write a mock with the same name as the original and link that instead. Whether you can generate that mock using your mocking framework in the normal way, I'm not so sure.
If you like, I suppose it's a "very bad problem for C++" that it's possible to write code that's hard to test. It shares this "problem" with a great number of other languages...
[*] My Java knowledge is quite low-power. There may be some clever way of mocking such methods in Java, which aren't applicable to C++. If so, please disregard them in order to see the analogy ;-)