Kerr nonlinearity plays a pivotal role in nonlinear photonics. Recent advancement in wafer bonding techniques has led to the creation of a cubic silicon carbide-on-insulator (3C-SiCOI) platform with improved crystalline quality, offering exciting prospects for investigating the Kerr effect in 3C-SiC. In this paper, we demonstrate 3C-SiC's Kerr effects through design, fabrication, and experimental investigation. By using the cavity enhanced four-wave mixing based on microring resonator (MRRs) supporting transverse electric or magnetic (TE/TM) polarizations on the 3C-SiCOI platform, we experimentally retrieve the Kerr nonlinear index (n2) of 3C-SiC within diverse waveguide dimensions, revealing a value of 4.92 and 5.00 × 10−19 m2/W for TE and TM polarizations, respectively. We further confirm the thermal stability of the 3C-SiC in Kerr effects at elevated temperatures from 100 °C to 300 °C, showing negligible change of n2. Moreover, we demonstrated optical parametric oscillation (OPO) in the fabricated single mode MRR via a dual-pump configuration. With an input power of less than 50 mW, a distinct OPO spectrum covering the C band has been achieved. These results signify the emergence of 3C-SiCOI as a promising platform for Kerr applications.