Nobody knows for sure, as there were many songs written, but never released.

Do you want the titles of every solo song by every one of the Beatles from all over the world? You got all night?

Please, my friend, go to http://www.google.com and type in "Beatles songs" (without the quotes) and start clicking.
References :

This is a lost of all the songs by The Beatles, and it tells if they’re covers or if it was written by one of the Beatles.
http://en.wikipedia.org/wiki/List_of_The_Beatles_songs
References :
Great to see another Beatles fan!

They wrote songs together and individually – But the majority were penned by Lennon and McCartney

If you want further information you can look up each album on google or wikipedia and get your answers that way.

But this is a start:

1.) Introducing The Beatles — July 22, 1963

2.) Meet The Beatles! – January 20, 1964

3.) Introducing The Beatles – January 27, 1964 (Reissue)

4.) The Beatles Second Album – April 10, 1964

5.) A Hard Day’s Night – June 26, 1964

6.) Something New – July 20, 1964

7.) The Beatles’ Story – November 23, 1964

8.) Beatles ’65 – December 15, 1964

9.) The Early Beatles – March 22, 1965

10.) Beatles VI – June 14, 1965

11.) Help! – August 13, 1965

12.) Rubber Soul – December 6, 1965

13.) "Yesterday…And Today" – June 20, 1966

14.) Revolver – August 8, 1966

15.) Sgt. Pepper’s Lonely Hearts Club Band – June 2, 1967

16.) Magical Mystery Tour – November 27, 1967

17.) The Beatles (The White Album) – November 25, 1968

18.) Yellow Submarine – January 13, 1969

19.) Abbey Road – October 1, 1969

20.) Hey Jude – February 26, 1970

21.) Let It Be – May 18, 1970
References :