A number pattern is shown as

n^3 + 1 = (n + 1)(n^2 - n + 1)   ,   where ^ = raised to the power of

ie

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


find an expression for 8p^3 + 1

now I would start with

(8p + 1)(8p^2 - 8p + 1)

but the answer is

(2p + 1)(4p^2 - 2p + 1)

so what is the working to get to (2p + 1)(4p^2 - 2p + 1)

TIA

Doug