This week's book giveaway is in the OCAJP 8 forum. We're giving away four copies of OCA Java SE 8 Programmer I Study Guide and have Edward Finegan & Robert Liguori on-line! See this thread for details.
... you cannot extend from a class with only private constructors, but it is best to mark the class final so any users know it cannot be extended from. That class should only have static members. There is a section about it in the Java™ Language Specification.
If it is a singleton, or has factory methods, then it can be instantiated, albeit only locally to its own class. It said "not to ... instantiate" in the thread title. So I presumed it must be a utility class with static members only, like java.lang.Math, which only has a private constructor.