You can’t use any built-in integer type for this. You need a “multiple precision integer” aka “bignum” library. For C++, I would try Boost.Multiprecision first, but be aware that Boost can be considerably more trouble than it is worth, particularly if the module you’re using has any shared library (aka DLL) component. The other obvious choice is GNU MP. It only has a C interface, but it is well-maintained, reliable, fast, and very popular (in fact, it appears that Boost.MP is “just” a C++ wrapper for it!)
WARNING: You might want a bignum library because you are trying to implement one of the cryptographic primitives that uses huge numbers, like RSA. Do not do this. The generic bignum libraries are not safe for cryptographic use, and even if they were, there would still be dozens of subtle mistakes you can make that would ruin your security. Use a well-tested cryptography library instead; for C++ I recommend Botan.