Close but a bit bigger.
Time to give this a nudge.
It is a European cartridge that was used in both WW1&2. The cartridge in the photo is loaded with a modern projectile. Below is another cartridge in is more natural state.
Is it a 6.5mm cartridge?
No it is bigger than that. Your first guess was close.
8x52mmR Mannlicher?
8x50mmR Mannlicher.
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That’s the one. Your turn 
30-06 Whinchester Silvertip pill
nope. a little bigger
Is it a .444 Marlin?
Nope, smaller
Is it 8x57
Nope. Bullet diameter a little bigger still
338 Snipe-Tac or 338 Federal
Nope. Much older
Will give you all a hint, it’s named for its lands diameter rather than groove diameter.
What about a .408 Cheyenne Tactical?
no, smaller, less tactical, more safari