Gigantic Steed class ability gives all the benefits of a Huge mount?

As per title, I’m wondering whether the Gigantic Steed ability of the Mammoth Rider grants your mount all the benefits of a size increase, namely +8 Str. In fact, the text of the ability is:

A mammoth rider’s steed increases to Huge size. […] It also gains a +2 size bonus to its Strength and Constitution.

And then the bonuses to Str and Con increase over time with the Mammoth Rider class. So, for example, a standard Mastodon companion has a base str of 24, so by becoming Huge its str goes up to 26 (and then there are all the size modifiers to CMB, CMD, AC, Attack, etc). Am I correct?

Finally, I recall that a size increase from large to huge means +8 str, but I can’t find any confirmation in the books. Right now all I have is Animal Growth’s text and the fact that PCGen gives it a +8 str. Is there any standard reference for the matter?