Is it me or this is not the "same approach"? Correct me if i'm wrong but i think Arrays.stream.sum() iterates fron index a to b, so in every iteration of the for loop you are iterating again. Your algorithm is not 0(n) as @Saikumar_P's. This is my 0(n) solution with Java similar to @Saiumar_P's:

static int birthday(List s, int d, int m) {

    int[] sums = new int[s.size() + 1];
    int count = 0;

    for(int i = 0; i < s.size(); i++) {

        int sumsIndex = i + 1;
        sums[sumsIndex] = sums[sumsIndex - 1] + s.get(i);

        if (sumsIndex >= m && (sums[sumsIndex] - sums[sumsIndex - m]) == d)
            count++;
    }

    return count;       
}