Largest Deep Sum

Wolfram Language (Mathematica), 36 bytes

#~Position~Max@#&@Total[#,{-#2,-1}]&

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Returns an array containing all the indices where the maximum value can be found. So for normal inputs that's a singleton array, containing the list of indices to it. If there's a tie, you'll get all the lists of indices for where that value shows up.

The function doesn't actually read the n parameter, because it isn't needed, but you could pass it in as a third argument if you like (it would just be ignored anyway).

One catch here is that for some reason the dimension specification {0,-1} for Total never sums anything. I don't really understand why, but luckily that's just what we need for this challenge.

APL (Dyalog), 21 bytes

(⍴⊤⊃∘⍒∘,)+/,⍤⎕⊢⎕

First input is the array, second is p.

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How?

+/,⍤⎕ - apply sum over sub arrays of rank p

⊃∘⍒∘, - flatten, grade down and take first

⍴⊤ - encode in the mixed base derived by the shape of the previous result