HowHome many bales does he have to have

Paul's answer is certainly a good one, and correct; however, there is another way to look at this, in addition to the 1-squared (1x1), 2-squared (2x2), etc as Paul pointed out. You could look at it as the number of units (bales of hay) each level increases by 1, 3, 5 (and continuing from Level 4-8), 7, 9, 11, 13, 15, 17; in other words, the bales are increasing by odd numbers. The next level (4) will increase by 7; add 7 to the prior level total of 9 -- 7 + 9 = 16. Add 9 to this total for the next level -- 9 + 16 = 25. And so on.

So, to answer your question - how many bales of hay does he have -- 1 + 4 + 9 + 16 + 25 + 36 + 49 + 64 = 204 total bales.

Paul's way of looking at it is more concise, but it's always good to see the problems from different angles :)