3D Gaussian Splatting (3DGS) enables high-quality real-time 3D rendering but faces challenges in efficiently scaling to ultra-dense scenes and high-resolution due to computational bottlenecks that limit its use in latency-sensitive applications. Instead of optimizing the splatting pipeline itself, we propose \textbf{3DGS$^3$}, a unified post-rendering framework that jointly performs super sampling and frame interpolation through differentiable processing of low-resolution outputs to achieve both high-resolution and high-frame-rate rendering. Our \textbf{Gradient\- \-Aware Super Sampling (GASS)} module leverages the continuous differentiability of 3DGS to extract image gradients that guide a GRU-based refinement network to enable high-fidelity super sampling. Furthermore, a \textbf{Lightweight Temporal Frame Interpolation (LTFI)} module based on a compact U-Net-like backbone fuses temporal and differentiable spatial cues from consecutive frames to synthesize temporally coherent intermediate frames. Experiments on public datasets demonstrate that 3DGS$^3$ achieves superior rendering efficiency and visual quality when compared with state-of-the-art methods and remains compatible with existing 3DGS acceleration techniques. The code will be publicly released upon acceptance.