A cubical 2-knot \(K^2\subset \mathbb {R}^4\) is an embedding of the 2-sphere in the 2-skeleton of the canonical cubulation of \(\mathbb {R}^4\) . In this paper, we describe cubical 2-knots in a discrete way, i.e., as a sequence of a finite number of points; in particular, we prove that there exists a generic projection \(p:\mathbb {R}^4\rightarrow P\) onto a suitable hyperplane P such that p(K) is a knot diagram and using this fact, we develop an algorithm to compute its fundamental group.