list = {{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.994429, 0.980929, 0.971825,
0.967241, 0.967241, 0.971825, 0.980929, 0.994429, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0.998888, 0.971825,
0.948683, 0.929755, 0.915302, 0.905539, 0.900617, 0.900617,
0.905539, 0.915302, 0.929755, 0.948683, 0.971825, 0.998888, 0, 0, 0,
0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0.971825, 0.939267, 0.910433,
0.885689, 0.865384, 0.849837, 0.839312, 0.834, 0.834, 0.839312,
0.849837, 0.865384, 0.885689, 0.910433, 0.939267, 0.971825, 0, 0, 0,
0, 0, 0, 0}}

list = Partition[Flatten[list], 3]

Total[Partition[list, {3, 3}], {3, 4}]

{{0, 0, 2.90998, 6.506198, 8.164602, 8.164602, 6.506198, 2.90998, 0, 0}}

array = Transpose /@ ArrayReshape[Transpose@list, {10, 3, 3}];
MatrixForm /@ array

Total /@ Flatten /@ array

Total /@ Flatten /@ ArrayReshape[Transpose@list, {10, 3, 3}]

BlockMap[Total[#, 2]&, list, {3, 3}]

Partition[list, {3, 3}, {3, 3}, None, {}, Plus]