Formula use: \left(a+b\right)^3=a^3+3.a^2.b+3.a.b^2+b^3

Explanation

Here, given equation is :
\left(5x+2y\right)^3+3\left(5x+2y\right)^2\left(x-2y\right)+3\left(5x+2y\right)\left(x-2y\right)^2+\left(x-2y\right)^3
Let,
\left(5x+2y\right)=a
\left(x-2y\right)=b
So that, we get :
a^3+3{.a}^2.b+3.a.b^2+b^3
\rightarrow\left(a+b\right)^3
Now, putting the value :
\{\left(5x+2y\right)+\left(x-2y\right)\}^3
\rightarrow\left(5x+2y+x-2y\right)^3
\rightarrow\left(6x\right)^3
\rightarrow 216x^3
Ans: 216x^3\ .