"Eight eights."
But because it's slightly unusual and easily misunderstood, I think you need to rely on creative description. Personally I would say something like "it is just the numeral 8 repeated 8 times: 8, 8, 8, 8, 8, 8, 8, 8." Or write it out on a scrap of paper.
"Eight times eight" is bad, because with that word order it sounds like multiplication, 8 x 8 = 64. They probably would not type in "64," but they might say "huh? What do you mean?"
"Eight eights" is good.
"Eight, eight times" is OK, because that's not how we express multiplication.
"Eight, repeated eight times" is better.