The expected value of a random variable raised to a power of more than two

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I have come across a question that asks me to find $E((1+X)^3)$. The only values given in the question are $E(X)$ and $E(X^2)$ and I tried to solve it by expanding $(1+X)^3$. But with this approach, I have an $E(X^3)$ term that I don't know how the find the value of. Any help would be much appreciated.

Edit: The values of $E(X)$ and $E(X^2)$ are 1 and 4 respectively.