To simplify the expression, let's break it down step by step:

1) First, let's simplify (-1/2)^3:
(-1/2)^3 = (-1/2) * (-1/2) * (-1/2) = -1/8

2) Next, let's simplify |-4/7|:
|-4/7| = 4/7

3) Now, let's substitute the simplified values back into the expression:
(16/49) + (-1/8) - (4/7) - (7/8)

4) Let's find a common denominator for the fractions:
The common denominator for 49, 8, and 7 is 1372.

5) Now, let's convert all the fractions to have the common denominator:
(16/49) * (28/28) + (-1/8) * (171/171) - (4/7) * (196/196) - (7/8) * (171/171)
= (448/1372) + (-171/1372) - (784/1372) - (1197/1372)

6) Now, let's combine the fractions:
(448 - 171 - 784 - 1197) / 1372
= (-1704) / 1372

7) Finally, let's simplify the fraction:
-1704/1372 = -426/343

Therefore, the simplified expression is -426/343.