Version 4.0.0 is large and often split into an APK (application) and an OBB (expansion file). Download both. The OBB file usually goes into Android/obb/com.smmwe.worldengine/ .

While 4.0.0 was a major release, newer maintenance builds have since been released to address bugs found in that version: SMMWE 3.4.4F V2 super mario maker world engine 4.0 0 apk