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0, 1, 4, 5, 6, and 9 can be the last digits of the squares of natural numbers.

Step-by-step explanation:

When looking at a list of the perfect squares, the last digits continuously follow this pattern: 1, 4, 9, 6, 5, 6, 9, 4, 1, 0. After this it repeats. This means that these are the only numbers that can be the last digits. When you take out the repeated numbers you get: 1, 4, 5, 6, 9, 0 which when written in order is:

0, 1, 4, 5, 6, and 9