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Photons have no invariant mass (the hypothetical mass they would have if they weren't moving, which cannot happen). So in that sense, light is massless.

However, light (and individual photons) have energy, and we know from Einstein's famous formula that energy is related to mass. (A different formula E=hv relates energy to frequency, so we can even calculate the precise equivalent mass for any given wavelength of light). In this sense, light has mass, and this can be shown by gravitational lensing, where a large enough concentration of mass can actually bend the path of light ... precisely as would be expected if light had mass.

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