apt-get install <pkg> first downloads the binary debian package to
/var/cache/apt/archives/ and then installs it. So you could theoretically copy binary debian pkgs from there and install them manually elsewhere. However, if the package depends on other packages, then you would also need to take steps to install them.
You may not want to do this because you will always be able to install the latest debian binary pkgs from the usual online archives (like for example archive.ubuntu.com), and they will always be more up to date regarding security fixes, feature enhancements, and etc.
Ubuntu archives are here: http://archive.ubuntu.com/
There are other online archives that host installable debian packages.