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(a+b\right)^3+\left(a-b\right)^3+3\left(a+b\right)^2\left(a-b\right)+3\left(a+b\right)\left(a-b\right)^2
Let,
x=\left(a+b\right)
y=\left(a-b\right)
Now, Simplify the equation :
\left(a+b\right)^3+\left(a-b\right)^3+3\left(a+b\right)^2\left(a-b\right)+3\left(a+b\right)\left(a-b\right)^2
Or, \left(a+b\right)^3+3\left(a+b\right)^2\left(a-b\right)+3\left(a+b\right)\left(a-b\right)^2+\left(a-b\right)^3
Now, putting the x & y value, we get :
x^3+3.x^2.y+3.x.y^2+y^3
\rightarrow\left(x+y\right)^3
\therefore Putting the value :
\{\left(a+b\right)+\left(a-b\right)\}^3
{\rightarrow\left(a+b+a-b\right)}^3
\rightarrow\left(2a\right)^3
\therefore 8a^3
Ans: 8a^3.