Range Sum - Building the Array

Building the prefix array takes one pass through the input:

function buildPrefixSum(nums)
    n := length of nums
    prefix := array of size (n + 1)
    prefix[0] := 0
    for i from 0 to n - 1
        prefix[i + 1] := prefix[i] + nums[i]
    return prefix

Time: $O(n)$. Space: $O(n)$.

Notice how each prefix value builds on the previous one. You're not recalculating sums from scratch each time.