What was the first Beatles song to be recorded using 8 track as opposed to 4 track equipment?

Quite likely it was "Hey Jude"

In 1968 eight-track recorders became available, but Abbey Road was somewhat slow in adopting the new technology and a number of Beatles tracks (including "Hey Jude") were recorded in other studios in London to get access to the new eight-track recorders

https://en.wikipedia.org/wiki/The_Beatles'_recording_technology

I did research other 1968 Beatles tracks, and the comments about recording methods do not mention 8 track.

https://en.wikipedia.org/wiki/The_Beatles_discography

"While My Guitar Gently Weeps"

From a technological standpoint, the White Album is significant for marking the Beatles' transition to eight-track recording. In this respect, Ken Scott, who replaced Emerick in the engineer's seat, played an instrumental role. Abbey Road had purchased several 3M eight-track recorders in May 1968, but the machines required numerous modifications before George Martin would approve their use on Beatles sessions. However, during an evening of work on ''While My Guitar Gently Weeps," Scott removed one of the unmodified eight-track machines from storage when he could no longer tolerate being limited to four tracks.

guitarworld.com/guide-beatles-white-album-recording-equipment-songs-conflicts webpage no longer exists

It was while these tests were being carried out that the Beatles recorded 'Hey Jude' and 'Dear Prudence' on eight-track at the independent Trident Studios in Central London. So, when George Harrison came across one of the 3Ms sitting in a corridor at EMI, he immediately told Ken Scott that the machine should make its way to the Studio Two control room, and Scott assigned tech engineer Dave Harries the task of ensuring this happened without being granted permission by the studio bosses ... The group's very first eight-track recordings at EMI were some of the overdubs on 'While My Guitar Gently Weeps'. This began life on four-track when, on 25th July, 1968, George Harrison rehearsed his new composition with his band mates before taping a solo version that was very different to that which ended up on the album ... It was on 22nd August, while recording 'Back In The USSR', that Ringo quit the band, and his return on 4th September to film the 'Hey Jude' and 'Revolution' promotional videos was a day after 'While My Guitar Gently Weeps' had been transferred to eight-track

https://www.soundonsound.com/people/beatles-while-my-guitar-gently-weeps

"While My Guitar Gently Weeps" seems to be the first Beatles track recorded on 8 track *at Abbey Road*.

"Hey Jude" was recorded, as stated above *at other studios*, three months earlier.

https://en.wikipedia.org/wiki/The_Beatles_discography

Just looking at wikipedia the answer out of the above two mentioned songs would be Hey Jude.

Hey Jude was recorded at Trinity studios on the 31st july - 2nd August 1968, and While My Guitar Gently weeps was recorded at Abbey Road 5-6 September 1968

https://en.wikipedia.org/wiki/While_My_Guitar_Gently_Weeps
https://en.wikipedia.org/wiki/Hey_Jude

This of course relies on these dates being the master tapes as the commercial release and no previous takes being credited or otherwise.

I just happened to come across this question, and so I'd like to note that it was definitively answered in the 2018 deluxe release of "The Beatles" double album, and the answer is indeed "Hey Jude", recorded at Trident on 31 July and 1 August 1968 and mixed there on 8 August. The Beatles had only intended to record the orchestra tracks there, because they had recorded the backing track in four track at Abbey Road on 29 and 30 July. Quoting from the album liner notes by Kevin Howlett:

[The] final Abbey Road mix was transferred to an eight-track tape at Trident Studios on 31 July. However, it was decided to record the song again. It was during this day that Paul's original line "She has found you now go and get her" was altered to "You have found her now go and get her". During the verses, George [who hadn't played on the four-track version] played a few linking passages on electric guitar. . . . The eight tracks on the tape of take one recorded at Trident consist of: track one: drums; two: piano; three: vocal and electric guitar in the first section then strings, clarinet and brass; four: John's acoustic guitar; five: piano, electric guitar, community singing, and handclaps; six: two electric guitars then brass instruments and strings; seven: bass guitar; eight: lead vocal, backing vocals, tambourine, and community singing.

The next Beatles recording in 8-track was "Dear Prudence", also at Trident on 28, 29, and 30 August (without Ringo, who quit the band that month; Paul played drums). And the delay in recording to lure Ringo back was what prompted Abbey Road to get its 8-track machine working for pop recordings (with modifications to the head block that were not needed when the machines were used for classical recordings), and The Beatles first used it to record the third (and final) fresh recording of "While My Guitar Gently Weeps" on 5 and 6 September 1968 and kept using it for the rest of the sessions.

Interestingly, The Beatles started recording on 8-track about a year after Mirasound in New York City had installed the first 16-track machine!