This is “sort of” possible, which I’ll explain, but the high number of times this question (or a very similar one about web page coding/displaying) is asked alarms me because it really shows a fundamental misunderstanding. What a large number of people seem to not understand is that Notepad++ is a Text Editor. As such, all it really does is allow you to edit text files, just like standard Notepad. Nobody would ever ask if standard Notepad can “build C++ files”.
So…you can edit your C++ source files (text files) in Notepad++. And you can setup some “helpers” that Notepad++ can use to invoke your C++ compiler and linker, and you can even set up Notepad++ to tell Windows to run your program and capture its output, but Notepad++ isn’t “building your C++ files” or “running” them…other things are doing that.
If you understand that, then the NppExec plugin is your key to setting up the helper that builds and runs your C++ code. Do some searching and reading about how that plugin works.