Title: Whopper whale
Description: Hard cover book, about 9"x11", maybe 24 pages. Singing fish on the inside covers.  Great color illustration on each page.  
I received mine as a gift when I was 3 or so (around 1956). I gave it away in a box of books about 25 years ago - and sorry I did. 

A boastful whale ("I have the biggest smile...the biggest frown...I'm a WHALE of a whale from my head to my tail. I'm a whopper, Whopper, WHOPPER!!") beaches himself while showing off to some little fish. Little boy rows around him in his boat and goes home to supper. Whopper finally frees himself by crying so many tears he raises the water level. He swims off, happy, wiser, and not so boastful.
Subjects: childrens story, whale
Time periods: Boastfulness ocean