Post number 5. I’m not sure if it’s actually part of the lyric or a count-off, though.
Manic Monday, the Bangles.
I believe that’s the first song beginning with six mentioned.
It’s lyrics, though probably adapted from the performances. Samudio called it Tex-Mex counting, maybe that was common in count-offs in Texas when he formed the band. But I’ve seen it in every representation of the lyrics. It’s critical to the song, people would start cheering as it started just from recognizing the sequence, and aside from the ‘Wooly Bully’ it’s about the only part of the lyrics people can understand.
“One, singular sensation every step she takes.” – “One” from A Chorus Line
“Three hits to the heart son, and it’s poetry in motion.” – “Three Hits” The Indigo Girls
“99 bottles of beer on the wall/99 bottles of beer…” (traditional)
“26 miles across the sea/Santa Catalina is a-waitin’ for me” (“26 Miles”, Four Preps, 1958)
“77 Sunset Strip” (TV show theme song, 1958)
“1,000,000 to 1/That’s what our folks think, about this love of ours” (“A Million to One”, Jimmy Charles, 1960)
“5-7-0-5!/But there’s no reply!” (“5.7.0.5”, City Boy, 1978)
“One pill makes you larger, and one pill makes you small…” (White Rabbit - Jefferson Airplane0
“Two of us riding nowhere, spending someone’s hard earned pay…” (Two of Us - the Beatles)
Honorable mention: “Nothing Compares 2 U” by Sinead O’Conner (“It’s been Seven Hours and Fifteen days…”) which is close.
Changing of the Guards by Dylan “Sixteen years
Sixteen banners united over the field
Where the good shepherd grieves…”
Roy Orbison, Ride Away: “Two wheels a-turnin’/One girl a-yearnin’”
Johnny Cash, Long Black Veil: “Ten years ago on a cold dark night/Someone was killed 'neath the town hall light.”
Elvis Presley, One Night: “One night with you/Is what I’m now praying for.”
The Beatles, I’ll Follow the Sun: “One day you’ll look/To see I’m gone”
Katrina- If Only — 3 AM Text Alert…
Rock Around The Clock, Bill Haley and His Comets
Ten Little Indians
“Sixteen Military Wives,” The Decemberists (“16 military wives / 32 softly focused brightly colored eyes”)
“Texarkana,” R.E.M. (“20,000 miles to an oasis / 20,000 years will I burn”)
“Bull in the Heather,” Sonic Youth (“10, 20, 30, 40 / Tell me that you want to hold me”)
Surprisingly few “Multiplication Rock” songs, which I still remember almost 40 years later:
2: “Elementary, My Dear” (“40 days and 40 nights / Didn’t it rain, children?”)
3: “Three is a Magic Number” (first line = title; also the sample in the aforementioned De La Soul song)
0: “My Hero, Zero” (“Zero?! / Yeah. Zero is a wonderful thing. In fact, zero is my hero.”)
I’m going to fudge a little with Golden Earring’s Twilight Zone.
“It’s 2 a.m.”
Hey, it’s almost the first word.
“73 men sailed up from the San Francisco Bay…” - Blues Image, Ride, Captain, Ride
Piano Man : “It’s nine o’clock on a Saturday…”
Safety in numbers.
If that counts, add the complete oeuvre of the Ramones to the list.
Sixteen men on a dead man’s chest
With a yo-ho-ho and a bottle of rum.
Do fractions and ordinal numbers count?
The Beatles, Julia: “Half of what I say is meaningless”
CCR, Someday Never Comes: “First think I remember was askin’ Papa why/For there were many things I didn’t know”
I can’t really claim Twilight Zone, though. It starts out with a spoken verse.
Somewhere in a lonely hotel room
There’s a guy starting to realize that eternal
Fate has turned its back on him.
It’s two a.m.
So I’m going to have to withdraw it.
U2’s “Vertigo” begins with “Uno, dos, tres, catorce…” – which is Spanish for “one, two, three, fourteen.”
Genesis “One for the Vine”: “Fifty thousand men were send to do the will of one…”
It’s not shown on lyrics sites, but Scorpions’ “Can’t Live Without You” begins with a standard countdown: “One, two, one, two, one two three four…”
Even if you ignore the spoken verse, the first word actually sung is “it’s.” 
Yeah, but I did admit right at the start that I was fudging it, and I would have stood behind it otherwise. In fact, I’ll back burpo up on Piano Man.