`P = a^3 + b^3 + c^3 - 3(a - 1)(b - 1)(c - 1)`

`= (a + b + c)[(a + b + c)^2 - 3sum_(cyc) ab] + 3abc - 3(abc - sum_(cyc) ab + a + b + c - 1)`

`= 3(3^2 - 3sum_(cyc) ab) - 3(abc - sum_(cyc) ab + 3 - 1) + 3abc`

`= 27 - 9sum_(cyc) ab - 3abc + 3sum_(cyc) ab - 6 + 3abc`

`= 21 - 6sum_(cyc) ab`

Có BĐT phụ sau(tự cm)

`sum_(cyc) ab <= ((a + b + c)^2)/3 = (3^2)/3 = 3 => - 6sum_(cyc) ab >= - 18`

`=> P = 21 - 6sum_(cyc) ab >= 21 - 18 = 3`

DBXR `<=> a = b = c = 1`