  In this note, we construct a $3$-dimensional generalisation of the Pascal's
triangle that we named Pascal's cube, as it has the construction of a cube with
entries given by extended binomial coefficients ${}^cC^{a}_{b}$. The Pascal's
cube is equivalent to the well-studied Pascal's pyramid, with the advantage
that the Pascal's cube can be mapped onto the Cartesian plane for easier
computation.
  We define a stochastic process using extended binomial coefficients on the
Pascal's pyramid representing the dispersion of a free particle. With some
constrains, we show that this stochastic process satisfies the heat equation.
