Here's a broad hint: First, do you know the identity

? It may be found in the Wikipedia article on Liouville's function, or as Theorem 300 in Hardy and Wright.

Next, write your sum as

Write out the first nine or so terms and collect together terms with , , and so on. Simplify, using the identity

where is the Riemann zeta function. You should end up with an expression that involves the identity that I mentioned at the beginning of this post (with s = 2). Finally, use the well-known identities

and

to arrive at the final answer.