Jelly, 16 bytes

³‘X’¤þ`ṂƤ€Z$⁺ṄS⁺

Try it online!

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_{I made a terrible mistake. No idea why no-one noticed that.}

Full program. Prints the array and the sum.

Not uniform, of course. Return all-zero most of the time.

Jelly, 16 bytes

³‘X’¤þ`ṂƤ€Z$⁺ṄS⁺

Try it online!

------

_{I made a terrible mistake. No idea why no-one noticed that.}

Full program. Prints the array and the sum.

Not uniform, of course. Return all-zero most of the time.

Verification for side length 2.

Jelly, 16 bytes

⁸‘X’¤þ`ṂƤ€Z$⁺ṄS⁺

Try it online!

_{Sorry, I forgot the "and the sum" part... Fixed now at +3 bytes.}

Full program. Prints the array and the sum.

Not uniform, of course. Return all-zero most of the time.

Jelly, 16 bytes

³‘X’¤þ`ṂƤ€Z$⁺ṄS⁺

Try it online!

------

_{I made a terrible mistake. No idea why no-one noticed that.}

Full program. Prints the array and the sum.

Not uniform, of course. Return all-zero most of the time.

Jelly, 16 bytes

⁸‘X’¤þ`ṂƤ€Z$⁺ṄS⁺

Try it online!

_{Sorry, I forgot the "and the sum" part... Fixed now at +3 bytes.}

Full program. Prints the array and the sum.

Not uniform, of course. Return all-zero most of the time.

Jelly, 16 bytes

⁸‘X’¤þ`ṂƤ€Z$⁺ṄS⁺

Try it online!

_{Sorry, I forgot the "and the sum" part... Fixed now at +3 bytes.}

Full program. Prints the array and the sum.

Not uniform, of course. Return all-zero most of the time.