The mammoth rider prestige class is the only class in the game that allows to have a Huge animal companion. The ability is described as follows :
Gigantic Steed (Ex)
A mammoth rider's steed increases to Huge size. The creature receives a –1 penalty on attack rolls and to AC, and a –2 penalty to Dexterity (to a minimum of 1); its base damage increases by one size category; and its reach increases to 10 feet. It also gains a +2 size bonus to its Strength and Constitution. At 3rd level and every two levels thereafter, the Strength bonus increases by an additional +2; the bonus to Constitution increases by an additional +2 at 5th and again at 9th level.
The mammoth rider has a limited list of animal companions available, all of them being Large at the point when this class is available to the player, then it's globally an increase by one size category with some ability score modifiers added.
According to the main rules, enlarging a creature from Large to Huge would increase its natural attack damage by one step, its reach by 5 ft, its CMB and CMD by 1 and its occupied space from 10x10 ft to 15x15 ft, reduce its AC by 1 and give extra penalties to attack rolls (-1), Fly checks (-2) and Stealth checks (-4).
In the case of Gigantic Steed, the penalty to attack rolls and AC, the extra reach and increase in natural attack damage are mentioned but nothing else is. Does this mean that Gigantic Steed only affects those numbers and everything else remains the same, including the creature's occupied space ?