Momentum isn't a function of mass it's a function of energy.
p = E/c
However, for the photons in the box, not all the photons are travelling in the same direction, so some of the momentum is cancelled out by photons moving in opposite directions, so E = pc wouldn't work because it doesn't take into account all the energy of the photons travelling in the opposite direction.
The formula involved in that interaction (with mass, of course) is:
p = gamma mv
gamma can therefore rationalised (this is junk-rigging here, do NOT write this on your finals) as a ratio of how much of the photons are contributing to the direction of travel (obviously a bit of a flimsy definition, but you get the idea). Let's say photons contributing to the direction of travel are q, and all the rest are Q.
Therefore gamma = q / Q
Since E = mc2 (E representing not total energy here, just the rest energy),
p = vqE /Qc2
v = velocity of the overall box, not of the individual photons (obviously that is just c)
For a beam of 'non-bound' energy, all the photons are moving in the the same direction, so for that q/Q = 1, and v = c, therefore p = E/c.
Again, that is jury rigging don't write that on your finals. But hopefully this jury rigged maths helps you understand how a bunch of photons in the box have momenta in various directions which can produce the "mass momentum" most people are familiar with.