Before we saw him drinking I assumed Exos didn't need sustenance, I assumed they were perfectly efficient machines or they drew energy from solar panels or something. But I guess their torsos have to be full of something that mimics a human digestive tract. Maybe they only eat and drink specific substances, hence Cayde's unnatural coloured drink in the trailer.
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They are completely inorganic. https://www.bungie.net/en/Forum/Post/227763711/0/0
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Inorganic doesn't mean they don't consume fuel in a similar manner to humans consuming food.
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You're right.