Finished translating Psalm 8 today, truly a great and important psalm.
[To the musician leading (those playing) the Gittith, a psalm (attributed) to David]
1 YHWH, our Lord, how magnificent [is] your name in all the earth,
[you] who put your splendor in the skies.
2 Through the mouth of boys and those nursing you arranged praise
because of your harassers, to stop the enemy and the revenger.
3 For I will look at your skies, the works of your fingers,
moon and stars, which you built.
4 What is humanity, that you remember it,
and the son of a human that you pay him attention?
5 You made him a little lower than God,
and [with] glory and honor you crowned him.
6 You made him to rule over the works of your hands;
you put everything under his feet.
7 Sheep and cattle, all them,
and also four legged animals of the plain.
8 Birds of the skies and fish of the sea,
things that pass through the paths of the seas.
9 YHWH, our Lord, how magnificent [is] your name in all the earth.
First, we read the psalm with a view to its original meaning using inductive Bible study methods. This means that we listen to the psalm in its own right and only with background information implied by the psalm itself. The headings were added later and thus cannot be used with any certainty to interpret the psalm itself inductively.
Sometimes we have good inductive reasons to conclude a heading is probably mistaken. In any case, since they are not part of the "original manuscript" of the psalm, they are not included in what is covered by terms like "inerrant" any more than textual variants like the ending of Mark is. The appropriate original meaning method is to read the psalm itself inductively and then see if its meaning seems to match the heading.
It is also inappropriate inductively to introduce information from elsewhere in the canon when interpreting the psalm. Each part of the Bible is incarnated truth, truth that comes within the language and usually the paradigms of its original context. As with the headings, we read the psalm inductively first and then branch out to other parts of the Bible.
Verses 4-8 are about the place of humanity in the created order. When one considers the grandeur of the skies and things like the moon and the stars, humanity seems so small. And yet God pays attention to us. Indeed, we are only a little lower than God in the created order. We cannot inductively be certain if the Psalm has Genesis 1 in mind, but the passage does remind us of Genesis 1:27-28 where humanity, both male and female, created in the image of God, rules over the creation. So also here humanity, made a little lower than God, rules over the works of God's hands, cattle, birds, fish, and so forth.
Literarily, the psalm is framed by an inclusio, in which the first and last verses bracket the psalm as a clear literary unit.
Fuller Sense ("sensus plenior")
The earliest Christians heard additional truths in this psalm. We cannot be certain if they heard the title "Son of Man" in the psalm, although it is possible. In general, one should not see more meaning in a text than is clearly indicated. Hebrews 2 does see Christ bringing the psalm to fulfillment. Humanity was created to have glory and honor but, presumably because of Adam (it is not 100% certain that Hebrews is thinking of him), humanity does not have everything under its feet.
So Jesus as human participates in the psalm and, presumably because he is without sin, makes it possible for humanity to fulfill it in the eschaton. These are of course not meanings the psalm originally had, but they are truths the early Christians heard in the psalm inspired by the Holy Spirit.
Although I cannot prove it, I like to think that Paul presupposes the sequence of thought in Hebrews 2. 1 Corinthians 15 assumes the Christ part of the equation. 1 Corinthians 15:20-28 blends together Psalm 110:1, which the early Christians read to be about God making Christ's enemies a footstool for his feet, with Psalm 8, where God puts everything under Jesus' feet.
For Paul, the one enemy yet to be put under Christ's feet is death. In the final resurrection, it shall also be conquered with finality.