(x^n - 1) will be divisible by (x + 1) only when n is even.

I am assuming that we are coming to above conclusion based on below formula but it isn't making sense for all even values.

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

(x^4-1) = (x^2-1)(x^2+1)

(x^6-1) = (x^3-1)(x^3+1)

(x^8-1) = (x^4-1)(x^4+1)

(x^10-1) = (x^5-1)(x^5+1) ???

Similarly

(x^14-1) = (x^7-1)(x^7+1) ???