Deep level nested list addition

I am doing a computation, it gives a nested list with a bunch of dimensions:

list={{{{1, 1, 1, 1}, {1, 1, 1, 1}, {1, 1., 1, 1}}, {{0, 0, 0, 0}, {0, 0,
0, 0}, {0, 0., 0, 0}}, {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0., 0,
0}}}, {{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0., 0, 0}}, {{0, 0, 0,
0}, {0, 0, 0, 0}, {0, 0., 0, 0}}, {{0, 0, 0, 0}, {0, 0, 0, 0}, {0,
0., 0, 0}}}, {{{1, 7, 17, 31}, {7, 7, 17, 31}, {17, -0.92, 1,
31}}, {{1, 4, 9, 16}, {4, 4, 9, 16}, {9, 0.04, 1, 16}}, {{0, 0, 0,
0}, {0, 0, 0, 0}, {0, 0., 0, 0}}}, {{{0, 0, 0, 0}, {0, 0, 0,
0}, {0, 0., 0, 0}}, {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0., 0,
0}}, {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0., 0, 0}}}, {{{1, 73, 433,
1441}, {73, 73, 433, 1441}, {433, 0.7696, 1, 1441}}, {{1, 52, 297,
976}, {52, 52, 297, 976}, {297, -0.1136, 1, 976}}, {{1, 16, 81,
256}, {16, 16, 81, 256}, {81, 0.0016, 1, 256}}}}


The list dimension is {5,3,3,4} in this example, but it can be other dimensions depending on computation.

But for this example, if I want to calculate the addition of each element that resides in the deepest level of the list in a "parallel" way.(The "parallel" is the only word I can think of to describe what will happen in terms of addition in my case.)

From my observations, I can treat my list as a multi-dimensioned array with 15 blocks, and each block has 3 X 4 elements, I am not sure if thinking in this way would be the best, but this is easy to understand:

So I want to add each of them all together to get a new list that its dimension should be 3 X 4 finally.

May I ask is there an good way to implement this?

Sorry for the irregular diagram , hope I describe my question well.

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