  In this paper, we study the {\it parabolic Anderson model} starting from the
Dirac delta initial data: \[ \left(\frac{\partial}{\partial t}
-\frac{\nu}{2}\frac{\partial^2}{\partial x^2} \right) u(t,x) = \lambda u(t,x)
\dot{W}(t,x), \qquad u(0,x)=\delta_0(x), \quad x\in\mathbb{R}, \] where
$\dot{W}$ denotes the space-time white noise. By evaluating the threefold
contour integral in the third moment formula by Borodin and Corwin [2], we
obtain some explicit formulas for $\mathbb{E}[u(t,x)^3]$. One application of
these formulas is given to show the exact phase transition for the
intermittency front of order three.
