Find the sum of `n` terms of the series `1.3.5.+3.5..7+5.7.9+...`

Explanation

The `n^(th)` term is `(2n - 1) (2n + 1) (2n + 3)`
`T_(n) = (2n - 1) (2n + 1) (2n + 3)`
`T_(n) = (1)/(8) (2n -1) (2n + 1) (2n + 3) {(2n + 5) - (2n - 3)}`
`=(1)/(8) (V_(n) - V_(n - 1)) " " [ " let " V_(n) = (2n - 1) (2n + 1) (2n + 3) (2n + 5)]`
`S_(n) = sum T_(n) = (1)/(8) [V_(n) - V_(0)]`
`S_(n) = ((2n - 1) (2n + 1) (2n + 3) (2n + 5))/(8) + (15)/(8) = n (2n^(3) + 8n^(2) + 7n - 2)`