Southern yellow pine can vary between 31.8 lb/cf to 38 lb/cf. Add in the weight of the treatment and adjust for the true size of the 8x8. That will give you an estimate of the weight.
For example, if the 8x8 was CCA treated to marine spec, you would add another 2.5 lb/cf to the weight. I think a nominal 8x8 is actually 7.5x7.5. If so, that means you'd adjust the total cubic nominal footage by .84 and then multiply the total actual cubic volume of the 8x8 by the total of the treatment weight and the density.