[@AtomicNut]

E=MC^2 declares that mass can be measured in energy, but also that the opposite applies. Effectively any particle that possesses energy must also possess mass. Energy in fact can be defined as mass measured in a different unit.

Photons are bent by gravity, but the effect of gravity on a particle is measured based on their mass. If photons truly possessed 0 mass then they would not be affected by gravity. However we know that light is bent by gravity ever since the effect of the sun's gravity well on the light of the stars was measured by Edward Eddington in 1919.

Invariant mass is measured as m = sqrt{E2/c4 - p2/c2} which returns that photons have no mass, and therefore light has no mass. However relativistic mass is defined by velocity.