We will consider a number of examples of Calabi–Yau threefolds defined over \(\mathbb Q\) having the Hodge numbers \(h^{p,q} = 1\) for all pairs \(p, q\) with \(p+q = 3\) (so \(B_3 = 4\)). Two of these Calabi–Yau threefolds are equipped with real multiplication by some real quadratic fields \(K = {\mathbb Q}(\sqrt{d})\) with square-free integers \(d > 1\), and satisfy the Hilbert modularity over \(K\). Starting with the Hilbert modularity over \(K\), we will establish the Siegel modularity over \(\mathbb Q\) of such Calabi–Yau threefolds that their (cohomological) \(L\)-functions coincide with the Andrianov \(L\)-functions of Siegel modular forms of weight 3, genus 2 on paramodular subgroups of level \(N\) of \(Sp(4, {\mathbb Q})\).