This paper examines unbiased Non-Data-Aided (NDA) Signal-to-Noise Ratio (SNR) estimation for hyper-cubic modulated signals in Additive White Rayleigh Noise (AWRN) channels. We investigate the Crame’r-Rao Lower Bound (CRLB) derivation, noting sensitivity to hyper-cubic constellation dimensions at low SNR. At higher SNR, we identify a unified behavior between multi-order square-QAM and hyper-cubic constellations, yielding a closed-form CRLB expression. Higher dimensions in hyper-cubic constellations increase the CRLB, mitigated by augmenting observations for improved precision. This study offers insights into optimizing SNR estimation precision across signal environments.