In recent years cubic silicon carbide (3C-SiC) has been regaining its importance among other SiC polytypes in development of various semiconductor device applications. Besides for active devices it can be used as a substrate for growth of high quality nitrides or epitaxial graphene layers. The quality of the latter greatly benefits from the absence of energy driven step bunching. The high electron mobility (~1000 cm2V-1s-1) and lower bandgap (~2.3eV) of 3C-SiC, compared to hexagonal SiC polytypes, enabled researchers to demonstrate the best channel mobility values (~300 cm2V-1s-1) among the SiC-based MOSFETs devices. The advantages of 3C-SiC for development of medium power devices have been recognized by the European Commission which is funding a collaborative research project ”CHALLENGE” (2017-2021) aiming at pushing 3C-SiC growth and device fabrication technologies closer to the market. There are also uprising innovative applications like intermediate band solar cells and photo electrochemical devices for water splitting which significantly benefit from the intrinsic 3C-SiC properties. Due to the lack of bulk 3C-SiC crystals, hetero-epitaxial growth on Si or hexagonal SiC substrates is the way used today to obtain 3C-SiC material with a size suitable for device fabrication. However, such 3C-SiC does not demonstrate the full potential of its intrinsic semiconductor properties due to a high density of defects, e.g. stacking faults, which are formed at the 3C-SiC/substrate interface. This problem is more pronounced in 3C-SiC grown on Si due to the large mismatch in lattice parameters and thermal expansion coefficients. Concomitantly, the majority of functioning devices, varying from MOSFETs to MEMS, have been demonstrated using such material. Therefore, it can be expected that mastering the growth and doping of 3С-SiC on hexagonal SiC substrates, especially providing high resistivity 3C-SiC material, would allow to demonstrate better performance of medium power devices. Although lattice and thermal matching between cubic and hexagonal SiC is not an issue, the 3C material quality on on-axis substrates is limited by the symmetry mismatch between SiC (0001) and 3C-SiC (111) , which induces rotational twinning and formation of double positioning boundaries (DPBs). Important fundamental problems on initial nucleation and defect formation have been already resolved and a solid background of knowledge has been delivered to developing of another 3C-SiC growth approach and that is to explore off-oriented hexagonal SiC substrates. In this talk we give a background of on-axis grown 3C-SiC and present results on growth of 3C-SiC crystals of superior structural quality using sublimation epitaxy. Bulk-like material with a thickness of about 1 mm and surface area of 10x10 mm2 can be reproducibly grown at temperatures below 2000oC in vacuum (10-5 mbar). The majority of growth studies were performed using 4H-SiC (0001) surfaces with the off-orientation of 4 degrees. In general, much higher density of steps on off-oriented surfaces, compared to on-axis, is a limitation in initiating 2D nucleation of 3C-SiC islands. However, under certain conditions a large facet/terrace can be formed at the edge of the substrate where an initial nucleation of 3C-SiC domains can be established. Upon growth progression, these domains enlarge laterally to cover the entire substrate surface with 3C-SiC. Such 3C-SiC substrates exhibit very high crystalline quality which was confirmed by HRXRD and LTPL analysis. The full width at half maximum (FWHM) value of ω rocking curves varied from 25 to 50 arc seconds. Typical defects in this type of growth are elongated domain boundaries which will be discussed. Unintentionally doped 3C-SiC layers with residual nitrogen concentration in a range of 1016 cm-3 exhibit resistivity of about 10-50 Ωcm. Such 3C-SiC substrates have been used for epitaxial growth of 3C-SiC and can be employed as seeds in sublimation bulk growth. We explored growth of intentionally B, Al, N and V doped 3C-SiC layers. The dopants were introduced by co-doping from the source material. We have demonstrated highly compensated 3C-SiC with resistivity close to 105 Ωcm range. I-V and C-V measurements of Schottky diodes fabricated on such material were used for the resistivity evaluation. SIMS and PL measurements have confirmed the presence of Vanadium. DLTS measurements are in progress for further identification of the deep levels. The growth issues related to dopants transfer as well as compensation mechanisms in high resistivity 3C-layers are discussed with special focus on V doped 3C-SiC material.