Formula use: \left(x+y\right)^3=x^3+y^3+3.\left(x+y\right).xy

Explanation

Here, given equation is :
\left(3a-7b\right)^3+\left(10b-3a\right)^3+9b\left(3a-7b\right)\left(10b-3a\right)
Let,
\left(3a-7b\right)=x
\left(10b-3a\right)=y

If we add x and y then we get :
\left(x+y\right)
\rightarrow\{\left(3a-7b\right)+\left(10b-3a\right)\}
\rightarrow\left(3a-7b+10b-3a\right)
\rightarrow 3b _——-(1)
Now, Simplify the equation :
\left(3a-7b\right)^3+\left(10b-3a\right)^3+9b\left(3a-7b\right)\left(10b-3a\right)
\rightarrow\left(3a-7b\right)^3+\left(10b-3a\right)^3+3.3b\left(3a-7b\right)\left(10b-3a\right)
\rightarrow\left(3a-7b\right)^3+\left(10b-3a\right)^3+3.\{\left(3a-7b\right)+\left(10b-3a\right)\}\left(3a-7b\right)\left(10b-3a\right) _{[from (1)]}
Now, putting the x & y value, we get :
x^3+y^3+3.\left(x+y\right).xy
\therefore\left(x+y\right)^3
\therefore Putting the value :
\left(3b\right)^3 _{[From (1), (x+y)=3b]}
\rightarrow 27b^3
Ans: 27b^3.