Is it possible to COMPLETELY delete a Book from my purchased books?

This has since moved from iTunes to within the iBooks app, but the procedure is exactly the same:

1. Open iBooks
2. Click iBooks Store in top-left corner
3. Click Purchased
4. Click the x in the top-left corner of the book you want to hide

And to unhide:

1. Open iBooks
2. Click iBooks Store in top-left corner
3. Click Account
4. Click Manage next to Hidden Purchases
5. Click Unhide below book in question

If this was bought through the iBooks store, then things will stay in your purchase history for as long as they are available to download. You can try to contact Apple and explain that it was your brother that made the purchase on your account and you want it removed. Also, have your brother pay you back too.

If this was just a web download then if you delete the file from your Mac and synced devices it will be gone and bother you no more.

It worked for me using iBooks on the Mac.

Go to the iBooks store. Top left.

Scroll all the way down and select "purchased"

From here you should see the books. Hover over and click the X in the left side. Works in Sierra.

so the answer is, No. it will be in the cloud permanently.