I have been trying to install FORM (https://github.com/vermaseren/form), and using the make command in cygwin in order to build it. However, I get the following error:
which is only the last part of the error, since the whole thing is approx. 10 times longer, but also filled with 'undefined reference to' errors.
My guess is that g++ has to be used instead of gcc, which is also installed in my case, but I don't know which command is the g++ equivalent for 'make'. Are there any other solutions that I am missing?

When you ask for support you should report the exact commands you gave and their output as text in line not as picture.
Please remember that
Makecalls the compilers, the compilers are producing the error you see. The root cause is that you have not properly configured the source for a compilation on Cygwin.The following is the build sequence that I used and that produced the proper binaries.
The build was not perfect but not so bad