Question: Prove $X_t = {W_t}^3 - 3\int^{t}_{0} W_s \, ds$ is a martingale using definition, that is, for any $0\leq s <t, $ we have $$\mathbb{E}(X_t|\mathcal{F}_s) = X_s$$ where $\mathcal{F}_s$ is the filtration generated by $X_s.$
I can solve the question by showing that the SDE satisfied by $X_t$ has no drift term, and thus $X_t$ is a martingale.
But I do not know how to show using definition of martingale.