My point was simply that he doesn’t use the same terminology as we do. Most of Philo’s original Greek was lost, but as far as I can tell, when he wants to describe a number times itself repeatedly, he doesn’t call it a power. In Greek he uses the word auxeseis, which would literally be translated “augmentation,” not dynamis, which is “power.” When he uses “power” he refers to some strengthened quality of the number. As your final quote shows, since a square is not the fourth power, nor is a cube the 8th power. But the number 4 is a “power,” in that the number 2 is empowered by augmenting it once (squaring it) to become 4, or twice (cubing it) to become the number 8, not the 8th power, but the powerful augmentation of 2 that becomes the number 8. The 8th power does not mean 2x2x2x2x2x2x2x2 but the number 8 as an empowered number by cubing 2.

That’s why he can say that 600 is a third, “minor” power of 6; it has nothing to do with 6x6x6, but 6 empowered twice, not augmented twice. It was just idle speculation on my part to say that it’s called a minor power because its name, hexakosios, is a diminutive of the name for 60, hexakontos, and both of those suffixes have to do with a minor and major “hurling,” which means throwing a number with force to a distant spot. In the same way that we say you “carry” the one in addition, they might say you “hurl” it. But that was just a guess on why those numbers have those names and why he called 600 a minor power. I see no indication that 60 was mentioned in that first passage for any reason other than to say that there’s a middle ground (not a mathematical mean/average) between 6 and 600. There was no contextual reason to mention 60 or to add 60 to the 6 or 600 to get 666, which he never mentions and has nothing to do with the Flood that he's discussing.

The wiki article you cited has footnote citations. The first one I checked specifically denies that dynamis, the Greek word that is translated as “power,” means power in the mathematical sense:

“dynamis is frequently translated as ‘power,’ but this translation is misleading–in fact it is downright false, for Greek mathematicians did not as yet have a general notion of ‘power.’ The Platonic term auxes comes close to our concept of ‘power’ but does not correspond to it, since there was only a second and third auxe in Greek.”

Reading a little farther in that same source, I see that he suggests "power" just means the value of any number after any transformation, so 600 is the third power of 6 in that 6 has been transformed twice in some way.