Let the two consecutive odd integers be (2n + 1) and (2n + 3). Then,

(2n + 3)² - (2n + 1)² = (2n + 3 + 2n + 1) (2n + 3 - 2n - 1)

     = (4n + 4) x 2

     = 8(n + 1), which is divisible by 8.