I am a newbie to Boost C++ libraries. I was wondering if there are any advantages of Boost bjam over GNU make? And what are the cons if I use make for building C++ code utilizing Boost.Python libraries?
For building boost itself, bjam is the way to go, by far. Just follow the readme and construct the command line. You may (should) only have to do it once per boost release.
But, there's no need whatever to tie your own project that uses boost to boost's build-system.
There are no particular cons to using gmake to build C++ code that uses Boost.Python, and the pro is that there are plenty of examples of using gmake around.