Looking at:

////////////////////////////////////////////////////////////////
//
// Calculate cubic volume based on Inside() method.
// Accuracy is limited by the second argument or the statistics
// expressed by the first argument.
// Implementation is courtesy of Vasiliki Despoina Mitsou,
// University of Athens.

G4double G4VSolid::EstimateCubicVolume(G4int nStat, G4double epsilon) const

One would expect the epsilon parameter to be used if one wants to guarantee the result with some given accuracy.

However, the parameter is unused, apart from one line without effect (apart from perhaps quell compiler warnings):

  if(epsilon > 0.01) epsilon = 0.01;

Cheers,
Thomas