Remote sensing image fusion aims to create a high-resolution multi/hyper-spectral image from a high-resolution image with limited spectral information and a low-resolution image with abundant spectral data. Recently, deep learning (DL) techniques have shown significant effectiveness in this area. Most DL-based methods approach image fusion as a 2D problem by encoding spectral information into feature map channels. However, our research suggests that this strategy introduces notable spectral distortions. In contrast, some methods consider spectral data as an additional dimension, utilizing standard 3D convolutions to preserve spectral information. Nevertheless, in a standard 3D convolutional layer, the same set of kernels is applied across all input regions, which we have found to be sub-optimal for image fusion. Furthermore, standard 3D convolutions necessitate substantial computational resources. To address these challenges, we propose a novel convolutional paradigm called Adaptive 3D Convolution (Ada3D) for remote sensing image fusion. Ada3D applies a unique set of 3D kernels to each input voxel, enabling the capture of fine-grained details. These adaptive kernels are generated through a two-step process: (i) spatial and spectral kernels are derived from their respective image sources; (ii) these two types of kernels are then combined to form content-aware 3D kernels that effectively integrate spatial and spectral information. Additionally, adaptive biases are introduced to enhance the convolutional outcome at the voxel level. Furthermore, we incorporate the group convolution technique to reduce computational complexity. As a result, Ada3D offers full adaptivity in an efficient manner. Evaluation results across five datasets demonstrate that our method achieves SOTA performance, underscoring the superiority of Ada3D. The code is available at https://github.com/PSRben/Ada3D.