2 + 5 + 6 = 13; 13² = 169
1 + 6 + 9 = 16; 16² = 256

8³ = 512; 5 + 1 + 2 = 8
27³ = 19683; 1 + 9 + 6 + 8 + 3 = 27

Passing through the quadrangle of Christ Church, Oxford, one day, the classical scholar Gilbert Murray encountered Albert Einstein sitting dreamily in thought.

Murray asked him what he was thinking about.

“I am thinking,” Einstein answered, “that, after all, this is a very small star.”

He who has not lost a thing has it.

You have not lost horns.

Therefore you have horns.

9 × 9 + 7 = 88
98 × 9 + 6 = 888
987 × 9 + 5 = 8888
9876 × 9 + 4 = 88888
98765 × 9 + 3 = 888888
987654 × 9 + 2 = 8888888
9876543 × 9 + 1 = 88888888
98765432 × 9 + 0 = 888888888

03/30/2017 UPDATE: Reader Alon Shaham points out that:

987654321 × 9 – 1 = 8888888888
9876543210 × 9 – 2 = 88888888888

You say that you have a dog.

Yes, and a villain of a one, said Ctesippus.

And he has puppies?

Yes, and they are very like himself.

And the dog is the father of them?

Yes, he said, I certainly saw him and the mother of the puppies come together.

And is he not yours?

To be sure he is.

Then he is a father, and he is yours; ergo he is your father, and the puppies are your brothers.

Let me ask you one little question more, said Dionysodorus, quickly interposing, in order that Ctesippus might not get in his word: You beat this dog?

Ctesippus said, laughing: Indeed I do; and I only wish that I could beat you instead of him.

Then you beat your father, he said.

— Plato, Euthydemus

2025 = (20 + 25)²
3025 = (30 + 25)²
9801 = (98 + 01)²