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Take a reaction like this

$$\ce{Fe^3+ + 3e- -> Fe}$$

now will the standard electrode potential change if we take 2 moles of $\ce{Fe^3+}$ and 6 moles of electrons?

$$\ce{2Fe^3+ + 6e- -> 2Fe}$$

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If you think of the Nernst equation, you'll see that: $$\Delta G° = -nFE°$$

Since $n$ corresponds to the number of electrons transferred, the ratio $\frac{\Delta G°}{n}$ remains constant, because any change in the stoichiometric coefficients will multiply both terms by the same value.

Therefore, we see that the potential is an intensive property, not depending on the dimensions of the system under study.

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