Values of n for which Integer Solutions to n = x^3 + y^3 + 2 z^3 are Unknown

Open Question
For the following values of $n$, it is not known whether the indeterminate equation:
 * $n = x^3 + y^3 + 2 z^3$

has any integer solutions:
 * $76, 148, 183, 230, 356, 418, 428, 445, 482, 491, 580, 671, 788, 931, 967$