How can something (ie. light) have volume and energy, but no mass?

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I’ve watched multiple YouTube videos and read a couple things online and now I have a headache. It still doesn’t make sense to me.
If photons have volume, then there can only be a finite number of photons in a given space, right? And once that limit is reached, why can’t I squeeze in one more photon? What is stopping me, the “walls” or “shell” of the photons? What are the walls/shells made of?

Every source I’ve looked at agrees that light is BOTH a wave AND a particle. I can understand why waves don’t have mass, but then what the hell is a “particle”? Every other elementary particle like quarks have mass, right?

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