let f(m)=m^3 + 3m^2 + 3m + 1

Question

notice f(-1) = 0, so m+1 is a factor.
Using division, the answer is m^2 + 2m + 1 which factors once more to (m+1)(m+1)

so you have (m+1)^3 = 0
and then m = -1

Are you familiar with Pascal's triangle?
Did you notice the pattern in the coefficients 1 3 3 1 and descending powers of m?

good work Reiny.

can anybody help with factoring this problem

m^3 + 3m^2 + 3m + 1 = 0

Does it help to check to see if -1 is a root? If so, x-1 can be divided into the polynomial.