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I know that Mega Mawile has a base attack stat of 105 and that huge power doubles their attack, not their base attack stat. This means that a fully invested Mega Mawile will have an attack stat of 678. I was wondering what mega mawile's base attack stat would be after the huge power boost.

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After the boost? You already said the answer: 678
Do you mean without huge power?

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If you take advantage of all the EVs and a +nature, then in order to reach an equivalent stat without the help of Huge Power, it would take a base stat of 259--so big that the system for encoding base stats can't store numbers that high.

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So if a Mawile with huge power, and no attack investment (Assuming 31 IVs in attack) it would have a whopping 492 attack.
That's mawile's attack, not its base attack stat.