To find the value of $x^2$, we need to solve the given equation and find the value of x first.

We are given that $64^3$ is equal to $8^x:$

$64^3 = 8^x$

We can rewrite 64 as $8^2:$

$(8^2)^3 = 8^x$

Using the power of a power property, we can simplify the equation:

$8^(2*3)$ = $8^x$

$8^6 = 8^x$

Since the bases are the same, the exponents must be equal:

$6 = x$

Now that we have found the value of x, we can substitute it into $x^2:$

$x^2 = 6^2 = 36$

Therefore, the value of $x^2$ is 36.

So, the correct answer is D. 36.