Q:

"Whatever/whatsoever book you like you can take it"? 

What is the difference between "whatsoever" and "whatever"? 
Which of them can be used in the following sentence:

Whatever book you like you can take it. 

Whatsoever book you like you can take it. 

A:

I've seen this confusion before and thought I knew the answer.  But when I wanted to cite some references, I was surprised. 
Whatever as a pronoun, adjective or determiner is defined as (LDOCE):

any or all of the things that are wanted, needed, or possible

and about 7 more definitions (available at the dictionary link I provided) that don't apply to the example given. 
But...
Whatever as an adverb:

used to emphasize a negative statement [= whatsoever]

And when you look up whatsoever:

used to emphasize a negative statement [= whatever]:

MW gives similar explanations for whatever and whatsoever. 
To answer your question directly: in your example you should definitely use whatever.  The word whatever has many meanings and it may be used instead of whatsoever.  But vice versa does not apply - in your example, you cannot use whatsoever because in this context whatever has another meaning.  Since there is a group of books to choose from, you might use whichever instead of whatever in this context. 

Whatever book you like, you can take it. 
Whichever book you like, you can take it. 
You can take whatever/whichever book you like.