data = Table[RandomReal[], {x, 1, 1000000}];
(* Method 1 *)
Timing[Total[Table[Total[ Table[data[[i]], {i, j, 10 + j}]], {j, 1, Length[data] - 5*10}]]]

(* Method 2, with constant index *)
m = 10;
Timing[Total[Table[Total[ Table[data[[i]], {i, j, m + j}]], {j, 1, Length[data] - 5*m}]]]

Timing[Total[Table[  (Total[ Table[data[[i]], {i, j, m + j}]])^2   , {j, 1, Length[data] - 5*m}]]]

Timing[Total[Table[Total[Table[data[[i]], {i, j, 10 + j}]], {j, 1,Length[data] - 5*10}]]]

m = 10;
Timing[Total[Table[Total[Table[data[[i]], {i, j, m + j}]], {j, 1, Length[data] - 5*10}]]]

With[{m = 10},
 Timing[Total[Table[Total[Table[data[[i]], {i, j, m + j}]], {j, 1,Length[data] - 5*m}]]]
 ]

a = With[{m = 10},
     Total[
      Table[Total[Table[data[[i]], {i, j, m + j}]], {j, 1,
        Length[data] - 5*m}]]
     ]; // RepeatedTiming // First
b = Total@ListCorrelate[ConstantArray[1., m + 1],
      data[[;; -50 + m - 1]]]; // RepeatedTiming // First
c = Plus[
     Range[1., m].data[[1 ;; m]],
     (m + 1) Total[data[[m + 1 ;; -5*m - 1]]],
     Range[N@m, 1., -1].data[[-5 m ;; -4 m - 1]]
     ]; // RepeatedTiming // First

a == b == c

m=10;
Total @ ListCorrelate[ConstantArray[1,m+1], data[[;;-50+m-1]]] //AbsoluteTiming