To calculate this expression, let's first convert the mixed numbers to improper fractions.

2 1/3 = 7/3
1 2/7 = 9/7

Now, multiply the two fractions:

(7/3 * 9/7) = (63/21) = 3

Now, cube the result:

3^3 = 27

Finally, multiply the result by 2/9:

27 * 2/9 = 6

Therefore, (2 1/3 • 1 2/7)в кубе • 2/9 = 6.