I assume that you meant "to mention the
past." Your sentence fragment as written implies someone who is still in his or her childhood. The use of "would" is as a conditional verb, the condition being the incomplete nature of said childhood without whatever books are specified in the completed sentence. For the sentence to "mention" the past, it would be necessary to use a past conditional form--"My childhood would have been
incomplete without the books of . . . "
It would be better, and more common in the expression of a native-speaker, to have written "Use of would to refer to the