A physics major, this is correct, in the sense that if the photons in the "matter of photons" have total energy E, then it acts like an object of mass m (under the condition that the total momentum is zero, which I presume is approximately true because the photons are moving in random directions?). However, photons do not have rest mass. The formula for photons is E = pc, where p is the momentum of the photon. The full form is E^2 = (mc^2)^2 + (pc)^2, where m is the rest mass and p is the momentum. Taking p = 0 for an object at rest gives E = mc^2, taking m = 0 for a photon gives E = pc.