Paul wasn't aiming for an album track, though; he was thinking of the song as the group's next single. The sessions for the album-in-progress had yielded two strong contenders from Lennon so far - No Reply and I'm A Loser - but these weren't really the stuff of singles from the Beatles in the latter half of '64, especially on the heels of the buoyant songs from A Hard Day's Night earlier in the year. Eight Days A Week would fit the bill perfectly.
But first, there was the little matter of writing and recording the song. The session on October 6th, 1964 was entirely devoted to the number, in part because Paul and John did not have the arrangement completely worked out in advance, particularly the introduction. Anthology 1 gives us a few variations of the intro including cascading "ooh"s by Paul and John, and a long, single "ooh" before we hear the full take five. This, too, has variations such as the way they sing the title line and some aggressive drum fills by Ringo.
Take six began with the instrumental introduction we all know (though played at full volume, of course) and had the boys settling on the way they wanted to sing the title line. After a brief break, multiple takes of overdubs began, the most notable being the handclaps and John's double-tracked vocal line, which is curious since the composition is primarily by McCartney.
They were still uncertain about the introduction as well as the ending of the song, which at this point was quite abrupt. At the start of a session on October 18th, Paul, John and George tried another take of "ooh"s as a new intro, but it was deemed insufficient. In his book Here, There and Everywhere, Geoff Emerick credits his predecessor as engineer Norman Smith coming up with the idea of simply fading up the intro as it presently stood. The band then approximated that introduction for a more rousing conclusion to the song. Later in this same session, a new Lennon song called I Feel Fine was recorded and chosen to be the next single, so Eight Days A Week suddenly wound up as an album track.
Capitol Records knew a single when it heard one, however, so the American label kept the song off of the album Beatles '65 (the US equivalent to Beatles For Sale) and held onto it for a few months, releasing it in February of '65 where it promptly became a number one hit.
Lennon was always dismissive of the song, despite his part in helping McCartney write it and the fact that his voice is the dominant one in the final mix. His opinion probably kept the number from making it into the group's live act. The one and only time that they promoted the song was on an appearance on the TV show Thank Your Lucky Stars taped on March 28th, 1965. They merely mimed their performance to the record and, as you can see in the photo at the top of this post, didn't even bother to plug in their guitars.