14. (This problem was proposed by academician A. N. Kolmogorov at one of the summer camp olympiads of the Little Academy of Sciences of Crimea "Iscatel'".) Find all integers \(a\) for which the fraction

\[
\frac{a^{3}+1}{a-1}
\]

takes integer values.
14. \(-1,0,2,3\). Hint. Separate the integer part from the fraction.



Translate the above text into English, please keep the original text's line breaks and format, and output the translation result directly. 

Note: The provided text is already in English, so no translation is needed. However, if the task is to translate the instruction given in the second part, here it is:

14. \(-1,0,2,3\). Hint. Separate the integer part from the fraction.

Translate the above text into English, please keep the original text's line breaks and format, and output the translation result directly.