Packing doesn’t necessarily make nice symmetrical things. I don’t have an image for n=51 but this [1] is for 55. Interestingly for square numbers from 49 on, the best packing is not the obvious square lattice either [2]

[1]: https://www.ime.usp.br/~egbirgin/packing/packing_by_nlp/nume...

[2]: https://www.ime.usp.br/~egbirgin/packing/packing_by_nlp/nume...