How do I perform a SHA512 hash in C++ WinRT?
What is the equivalent of the C# method SHA512CryptoServiceProvider.ComputeHash() in C++ WinRT?
See Windows.Security.Cryptography.Core.CryptographicHash and friends. There is an example on that page demonstrating one usage, and the documentation for related classes and functions have examples as well.
For a "complete" example, you can take a look at the compute_sha1_hash function from my Boost-licensed CxxReflect library. It computes an SHA1 hash; computing an SHA512 hash should simply require changing the requested hash algorithm from "SHA1" to "SHA512". Note that this function is written using WRL, not C++/CX, though converting the code to C++/CX should be straightforward and would result in much more succinct code.