Yes, the third vanishing point can be found just like the others. In 2-point perspective, vertical lines are flat and parallel in line with the viewer and converge at opposing vanishing points on the horizon line. In 3-point perspective, vertical lines also converge at a vanishing point, but that point is above or below the horizon line depending on if you can see the bottom or the top of the cube respectively.
Pay close attention to the veritcal lines of the cube. Even with one face, you can see how steep those lines are. Steeper convergence means the vanishing point is closer to the square, less convergence means it's farther away, and no convergence means 2-point perspective.