I am really confused about this example from my textbook. Here it is:

Suppose that we start with the universe that comprises only the 13 integers 2, 4, 6, 8,..., 24, 26. Then we can establish this statement:

For all n (meaning n = 2, 4, 6,..., 26), we can write n as the sum of at most three perfect squares.

The results in this table provide a case-by case verification showing the given (quantified) statement to be true. (We might call this statement a theorem.):

(Imagine these are in a table with 3 columns - I wasn't sure how to form tables in this)

2 = 1 + 1

4 = 4

6 = 4 + 1 + 1

8 = 4 + 410 = 9 + 1

12 = 4 + 4 + 4

14 = 9 + 4 + 1

16 = 16

18 = 16 + 1 + 120 = 16 + 4

22 = 9 + 9 + 4

24 = 16 + 4 + 4

26 = 25 + 1

This exhaustive listing is an example of a proof using the technique we call, rather appropriately, the method of exhaustion. This method is reasonable when we are dealing with a fairly small universe. If we are confronted with a situation in which the universe is larger but within the range of a computer that is available to us, then we might write a program to check all of the individual cases.

(Note that for certain cases in the table, more than one answer may be possible. For example, we could have written 18 = 9 + 9 and 26 = 16 + 9 + 1. But this is all right. We were told that each positive even integer less than or equal to 26 could be written as the sum of one, two, or three perfect squares. We were not told that each such representation had to be unique, so more than one possibility could occur. What we had to check in each case was that there was at least one possibility.)

My question: Why does it stop at 26 and not 28?