How to copy a file to multiple directories using the gnu cp command

You can't do this with cp alone but you can combine cp with xargs:

echo dir1 dir2 dir3 | xargs -n 1 cp file1

Will copy file1 to dir1, dir2, and dir3. xargs will call cp 3 times to do this, see the man page for xargs for details.

No, cp can copy multiple sources but will only copy to a single destination. You need to arrange to invoke cp multiple times - once per destination - for what you want to do; using, as you say, a loop or some other tool.