I think I'm going to block this person on Facebook.
why do you want to block him ?
I get so annoyed when he posts about his cancer patient status on facebook
That seems like a rather insensitive reason to block someone, but it's up to you who you want to be in contact with on social media. You don't have to be friends with someone you don't want to on Facebook. Just keep in mind that if you block him, your relationship with him may become awkward.
I don't care, I'm sick of his posts.
If you're sick of seeing his posts, then there's no reason to subject yourself to them any further. Just block him and move on with your life.