Modeling of high-frequency outgoing radiance distributions has long been a key challenge in rendering, particularly for glossy material. Such distributions concentrate radiative energy within a narrow lobe and are highly sensitive to changes in view direction. However, existing neural radiosity methods, which primarily rely on positional feature encoding, exhibit notable limitations in capturing these high-frequency, strongly view-dependent radiance distributions. To address this, we propose a highly-efficient approach by reflectance-aware ray cone encoding based on the neural radiosity framework, named neural cone radiosity. The core idea is to employ a pre-filtered multi-resolution hash grid to accurately approximate the glossy BSDF lobe, embedding view-dependent reflectance characteristics directly into the encoding process through continuous spatial aggregation. Our design not only significantly improves the network's ability to model high-frequency reflection distributions but also effectively handles surfaces with a wide range of glossiness levels, from highly glossy to low-gloss finishes. Meanwhile, our method reduces the network's burden in fitting complex radiance distributions, allowing the overall architecture to remain compact and efficient. Comprehensive experimental results demonstrate that our method consistently produces high-quality, noise-free renderings in real time under various glossiness conditions, and delivers superior fidelity and realism compared to baseline approaches.