I suggest you use
rsync rather than
cp to backup data as you want to do it. Rsync has a few options to deal with symlinks. A sym(bolic) link is simply a link to another file. It is a bit like a 'shortcut' in windows language.
-l, --links copy symlinks as symlinks
-L, --copy-links transform symlink into referent file/dir
--copy-unsafe-links only "unsafe" symlinks are transformed
--safe-links ignore symlinks that point outside the tree
-k, --copy-dirlinks transform symlink to dir into referent dir
-K, --keep-dirlinks treat symlinked dir on receiver as dir
-H, --hard-links preserve hard links
Here is an easy example:
sudo rsync --verbose --recursive --links --perms --executability --owner --group --times /media/some-user-name/the-c-drive-you-want /media/some-user-name/the-external-drive
Use the option
--dry-run for a hypothetical run that does not write anything to your external drive.
man rsync for more information on the different options.