The division of (m^3 - 6m^2 - 16m + 63) ÷ (m - 7) can be performed using polynomial long division. Here's the process:
m^3 - 6m^2 - 16m + 63
_________|_________
m - 7
m^2 - 13m + 63
_________|_________
m - 7
m^2 - 20m + 63
_________|_________
m - 7
m^2 - 20m + 56
Therefore, the division result is m^2 - 20m + 56 with a remainder of 0. So, the final answer is (m^2 - 20m + 56).