Formula use: \left(a+b\right)^3=a^3+b^3+3.a.b\left(a+b\right)
Formula use: \left(a+b\right)^3=a^3+b^3+3.\left(a+b\right).ab

Explanation

Here, given equation is :
\left(3-7m\right)^3+\left(8m-1\right)^3+3\left(m+2\right)\left(3-7m\right)\left(8m-1\right)
Let,
\left(3-7m\right)=a
\left(8m-1\right)=b
If we add a and b then we get :
\left(a+b\right)
\rightarrow\{\left(3-7m\right)+\left(8m-1\right)\}
\rightarrow\left(3-7m+8m-1\right)
\therefore\left(m+2\right) _——(1)
Now, Simplify the equation :
\left(3-7m\right)^3+\left(8m-1\right)^3+3\left(m+2\right)\left(3-7m\right)\left(8m-1\right)
\rightarrow\left(3-7m\right)^3+\left(8m-1\right)^3+3.\{\left(3-7m\right)+\left(8m-1\right)\}.\left(3-7m\right)\left(8m-1\right) _{[(a+b)=(m+2)]}
Now, putting the a & b value, we get :
a^3+b^3+3.\left(a+b\right).ab
\therefore\left(a+b\right)^3
So that, Putting the value :
\left(m+2\right)^3 _{[from 1, (a+b)=(m+2)]}
Or, m^3+\left(2\right)^3+3.m.2.\left(m+2\right)
Or, m^3+8+6m.\left(m+2\right)
\therefore m^3+8+6m^2+12m
Ans: m^3+6m^2+12m+8\ .