Easier than It Looks

Number Theory Level 2

There are four three digit natural numbers that satisfy the condition that each the sum of the cubes of its digits.

Here are the three of these numbers:

\[ \begin{eqnarray} 153&=&1^3+5^3+3^3 \\ 370&=&3^3+7^3+0^3 \\ 407&=&4^3+0^3+7^3 \\ \end{eqnarray} \]

Can you find the remaining missing number?


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