For a B777-200/200ER/300 at CI=85 at OPTIMUM level and Nil Wind, a Climb / Cruise Mach of 0.835 is typical. In the same conditions, M0.84 is more typical for the B777-300ER.
Naturally, cruise at Off-Optimum levels, and wind component, will change these 'ball-park' figures.
Regards,
Old Smokey