Three series I, II, and III following a certain pattern are given below. In the series, one of the numbers is missing in the numbers in series I, in series II, and in series III are represented by 'x', ''y', and 'z' respectively. 

Series I: 5, 61, 213, 509, _____, 1725, 2741

Series II: 1625, 1576, 1529, 1484, 1441, _____, 1361

Series III: 964, _____, 972, 984, 1004, 1034, 1076

Which of the following equation(s) is/are correct? 

I. 563 + y - (x + z) = 0

II. (x + 250) + (y + 130) = 3000- z

III. (x + y + z) = 58²