Simon Z.

grid = [[ 0,  1,  2,  3],
        [ 4,  5,  6,  7],
        [ 8,  9, 10, 11],
        [12, 13, 14, 15]]

# 4 for this grid, otherwise len() works
res = [[0] * 4 for i in range(4)]

# use this function to avoid bounds checking
def is_neighbor(x1, y1, x2, y2):
    if (x1 == x2 + 1 and y1 == y2) or (x1 == x2 - 1 and y1 == y2) or (x1 == x2 and y1 == y2 + 1) or (x1 == x2 and y1 == y2 -1):
        return True
    else:
        return False

# add numbers arounds point (x,y), including itself
def add_up(x, y):
    tf_map = [[0] * 4 for i in range(4)]
    for i in range(4):
        for j in range(4):
            if is_neighbor(x, y, i, j):
                tf_map[i][j] = grid[i][j]
    tf_map[x][y] = grid[x][y]
    sum = 0
    for row in tf_map:
        for item in row:
            sum += item
    res[x][y] = sum
    return res

# reconstruct the 2-D list
for i in range(4):
    for j in range(4):
        add_up(i, j)

print(res)
>>
[[5, 8, 12, 12], [17, 25, 30, 27], [33, 45, 50, 43], [33, 48, 52, 40]]