  In this communication with computer simulation we evaluate simple cubic
random-site percolation thresholds for neighbourhoods including the nearest
neighbours (NN), the next-nearest neighbours (2NN) and the next-next-nearest
neighbours (3NN). Our estimations base on finite-size scaling analysis of the
percolation probability vs. site occupation probability plots. The
Hoshen--Kopelman algorithm has been applied for cluster labelling. The
calculated thresholds are 0.1372(1), 0.1420(1), 0.0976(1), 0.1991(1),
0.1036(1), 0.2455(1) for (NN + 2NN), (NN + 3NN), (NN + 2NN + 3NN), 2NN, (2NN +
3NN), 3NN neighbourhoods, respectively. In contrast to the results obtained for
a square lattice the calculated percolation thresholds decrease monotonically
with the site coordination number z, at least for our inspected neighbourhoods.
