A Nasik (= pandiagonal & pantriagonal) 14x14x14 magic cube does not exist. Above simple, only a pantriagonal 14x14x14 magic cube has been constructed. Theoretical it is possible to get a diagonal 14x14x14 magic cube.
Simple (diagonal trial)
[Composite 2'] See the result of my 14x14x14 diagonal trial. It is simple magic and half of the diagonals in and through the levels give magic sum +/+ 49 and the other half give magic sum -/- 49. There are possibilities to fix some diagonals by swapping numbers, but to get a fully diagonal 14x14x14 magic cube ...
[Method of Luyendijk] I used the method for double odd order and I have constructed a pantriagonal 14x14x14 magic cube.