The original meaning of the Hebrew word "אלהים" (elohim) is "mighty one[s]", which may be just an ordinary plural or a majestic plural used in a singular sense. It really means nothing more than that. Certainly, the Hebrews used "אלהים" mostly for God, because after all God is viewed as the most mighty one of all, but given its broader meaning it is no surprise to see them use the word for other beings including humans and God's messengers.
The "מ" in front is a prefix, not part of the lexical unit "אלהים" itself, so you should not be talking about translation of "מאלהים" as "gods". Together, it means roughly "from mighty one[s]" which as a reference point for comparison means "than mighty one[s]".
Thus Psa 8:6 literally says nothing more than "and you make him a little less than mighty one[s]". Now what does this refer to? One must look at the context. The LXX interpreted it to refer to messengers (αγγελοι) of God, hence it puts "βραχυ τι παρ αγγελους" (somewhat a little less than messengers [of God]). The ASV preferred interpretating it as God himself, hence they put "God" in the main translation. Darby's translation matches the LXX, putting "angels".
It is clear that Psa 8 is praising God for the great works of his hands and yet giving 'insignificant' mankind authority over many of his works, and I think it makes little sense for the psalmist to say "a little lower than God" in such a psalm. The LXX reading makes more sense; although mankind was created as 'lower beings' compared to the messengers of God, they were given more authority; less might but more authority.
I agree with another answer that theology obscures or twists the reading of the text. I also agree that there does not seem to be an example in the Hebrew writings where "אלהים" unambiguously refers to angels, but still, it makes no sense to me to say "a little less than God". Firstly, everything that God creates is of course lesser. And secondly, "a little less" makes little sense given the preceding verses that imply that man is powerless (babies, infants, nothing intrinsically worth being mindful of). Even "the complete Jewish bible" renders Psa 8:6 using "angels"...