For any integers $i$ and $j$ such as $1\le i<j\le6$, let $x_{ij}$ be a real number. 

Is it true that, given the condition  
$$\sum_{1\le i<j\le6}x_{ij}^2=1,$$
the sum 
$$\sum_{1\le i<j<k\le6}x_{ij}x_{ik}x_{jk}$$
is maximized when all the $|x_{ij}|$'s are the same?