# Sum of Reciprocals of Cubes of Odd Integers Alternating in Sign in Pairs

 $\displaystyle \frac 1 {1^3} + \frac 1 {3^3} - \frac 1 {5^3} - \frac 1 {7^3} + \cdots$ $=$ $\displaystyle \frac {3 \pi^3 \sqrt 2} {128}$