  We give a generalization of the well-known result of E. Cartan on
isoparametric cubics by showing that a homogeneous cubic polynomial solution of
the eiconal equation $|\nabla f|^2=9|x|^4$ must be rotationally equivalent to
either $x_n^3-3x_n(x_1^2+...+x_{n-1}^2)$, or to one of four exceptional Cartan
cubic polynomials in dimensions $n=5,8,14,26$.
