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

Explanation

Here, given equation is :
\left(2a+3b\right)^3+\left(2a-3b\right)^3+12a\left(4a^2-9b^2\right)
Let,
x=\left(2a+3b\right)
y=\left(2a-3b\right)
Now, if we add x and y then we get :
\left(x+y\right)=\left(2a+3b\right)+\left(2a-3b\right)
\rightarrow\left(x+y\right)=\left(2a+3b+2a-3b\right)
\therefore\left(x+y\right)=4a _—–(1)
Now, Simplify the equation :
\left(2a+3b\right)^3+\left(2a-3b\right)^3+12a\left(4a^2-9b^2\right)
\rightarrow\left(2a+3b\right)^3+\left(2a-3b\right)^3+3.4a.\{\left(2a\right)^2-\left(3b\right)^2\}
\rightarrow\left(2a+3b\right)^3+\left(2a-3b\right)^3+3.4a.\{\left(2a+3b\right)\left(2a-3b\right)\}
Now, putting the x & y value, we get :
x^3+y^3+3.4a.\left(xy\right)
Or, x^3+y^3+3.\left(x+y\right).xy _{[put the ‘4a’ value,(1)]}
Or, \left(x+y\right)^3
\therefore Putting the value :
\{\left(2a+3b\right)+\left(2a-3b\right)\}^3
\rightarrow\left(2a+3b+2a-3b\right)^3
\rightarrow\left(4a\right)^3
\therefore 64a^3
Ans: 64a^3\ .