Spherical hohlraums (in particular hohlraums with octahedral laser entrance holes (LEH) [1]) are an alternative to the cylindrical hohlraums currently considered for inertial confinement fusion at NIF (U.S.A) and LMJ (France). These spherical hohlraums are advantageous from the point of view of the uniformity in the irradiation of the fusion capsule. Due to their octahedral symmetry, low-order spherical harmonics (P2, P4) cancel intrinsically. However, they are not advantageous from an energetic point of view, basically due to the radiation loses through their numerous LEHs. However, it is difficult to assess the net balance of these advantages and disadvantages, because, unlike cylindrical hohlraums, they cannot be consistently analyzed with 2D simulation codes. To achieve this goal, a new version of the MULTI-3D simulation code [2] has been developed. MULTI-3D is three-dimensional numerical simulation code for radiation hydrodynamics that includes: ALE hydrodynamics, Sn radiation transport with multi-groups, and ray-tracing laser deposition. Using this code, the analysis of different aspects of these targets have been carried out, putting special emphasis in phenomena that are not accessible with 2D modeling. The energetic efficiency of laser to radiation conversion is quantitatively analyzed. This depends on factors such as the size of the LEH, the density of the filling gas,  the orientation of the laser beams, and the location of the laser spots. Also the symmetry of capsule irradiation has been dynamically evaluated. In these targets, because laser beams impinge the internal walls of the cavity with a very oblique angle, the expansion of the plasma considerably moves the locations where the primary X-rays are generated. In addition, due to the complex distribution of laser hot spots, mutual iterations occur where plasma bubbles produced by a given beam intersect the trajectory of other beams giving place to secondary hot spots. This effect can even generate premature LEH closing if some laser spots are located near a LEH.