Go to your Android Settings > Security (or Privacy) and toggle on "Install unknown apps" or "Unknown sources" . This allows you to install apps outside of the Google Play Store.

The APK successfully ports the art style, character sprites, and some of the original audio.

If you want to experience Cuphead on your Android phone or tablet without risking your data security, you should avoid random APK sites entirely. Instead, use official services to stream the real game to your device: Xbox Cloud Gaming (Xbox Game Pass Ultimate)