Discrete Fourier Series of square of a signal
Here is an outline (in case it's homework)


Use a different frequency index for $X_2(l)$
Split the $X_2(l)$ into two sums: from $0:N-1$ and from $N-1:2N$
Use the periodicity of x[n], i.e.  $x(n) = x(n+N)$
Substitute $m = n-N$ in the second sum
Recombine the two sums again
Stare what happens to even $l = 2k$ and odd $l = 2k+1$ terms