Although I'm inclined to agree with KRyan, if you do want a more hard-and-fast rule of thumb...
A litre of water weighs roughly 1kg. Multiply that by 8000 and you've got, well, 8000kg of space. Obviously, you're probably going to be using that space to store precious metals like gold (treasure) or steel (weapons), so using the density of gold...
gold is very dense: a cubic meter has a mass of 19,300 kg. By comparison, the density of lead is 11,340 kg/m3.
If my math is right, 282 cubic feet is around 85 cubic meters, so a portable hole filled with gold would be 1,640,500 kg.
What if you want to store something other than gold? Well, the same Wikipedia page states that the densest element (osmium) is around 22 kg/m3. Gold's a good benchmark for the heaviest stuff an adventurer might store in a portable hole.
So yeah, you can pretty much throw the whole weight thing out the window at that point.
EDIT: So, it looks like there is some confusion as to my rationale for the calculations that I did. My original thought upon seeing the question was, "Is there a way to find out how much a solid mass of the dimensions of a portable hole weighs? If so, then you can use that to gauge how much stuff fits in the hole, because D&D items have weight/encumbrance." Unfortunately, different materials have different weights/densities, so I tried to calculate the upper limit that you might see if the hole was full of the heaviest stuff an adventurer might carry; specifically, gold. That way, it would be possible to illustrate that the amount/weight that would fit in the hole was so massive that it was really a non-issue. In other words, any specific thing that weighed enough to take up a decent chunk of the available weight (like a dragon or an elephant) would also probably be so large that it wouldn't fit in the dimensions of the hole, and anything smaller (like coins or other treasure) would take up so little volume that you'd be able to carry as much as any adventurer would be likely to ever have.