  The aim of this paper is to define cubic Dirac operators for colour Lie
algebras. We give a necessary and sufficient condition to construct a colour
Lie algebra from an $\epsilon$-orthogonal representation of an
$\epsilon$-quadratic colour Lie algebra. This is used to prove a strange
Freudenthal-de Vries formula for basic colour Lie algebras as well as a
Parthasarathy formula for cubic Dirac operators of colour Lie algebras. We
calculate the cohomology induced by this Dirac operator, analogously to the
algebraic Vogan conjecture proved by Huang and Pand\v{z}i\'c.
