How do I cancel my apple account?

You can deactivate the account or delete it.

Apple ID - How to deactivate your Apple ID account.    

All purchases made using an Apple ID are tied to the ID. Delete the ID and you will need to download them using your new ID. There have been posts by people who have contacted Apple Support and they were told that if you delete an ID associated with an email address, you can never reuse the email address for an Apple ID.  Make sure you sign out from the places in the 4th link before deleting the ID. If you fail to sign out of your device before deleting the ID, the device may become useless.

How to delete your Apple ID account.         

Apple ID – How to Delete.        

Delete Apple ID (new).         

What to do after you change your Apple ID or password - Apple Support