I found these sales (up to Feb 2010)
Source
I think they're accurate. Y'all should start a receipts thread for Cher, she deserves it. I'm not a stan so I wouldn't really want to make it unless I was invested in the artist.
Anyways.
Studio:
All I Really Want To Do (1966) — 750.000
The Sonny Side Of Cher (1966) — 750.000
Cher (1966) — 1.000.000
With Love (1967) — 500.000
Gypsys, Tramps & Thieves (1971) — 1.500.000
Foxy Lady (1972) — 500.000
Half-Breed (1973) — 1.500.000
Take Me Home (1979) — 1.000.000
Cher (1987) —1.500.000
Heart Of Stone (1989) — 6.500.000
Love Hurts (1991) — 3.500.000
It s A Man s World (1996) — 1.000.000
Believe (1998) — 11.500.000
Living Proof (2001) — 1.500.000
Compilation:
Cher Superpak (1972) — 300.000
Cher s Greatest Hits 1965-1992 (1992) — 2.500.000
Greatest Hits (1998) — 5.000.000
The Very Best Of Cher (2002) — 4.000.000
Total — 44.800.000. So with her latest release, she's definitely above 45M albums. I don't know if there are more albums that she's released since I'm not well-acquainted with her entire discog + Sonny & Cher sales are missing, but this is a good way to start off w/ estimates!