Basically the GBA has no builtin support for 3D. This is unlike the DS (and modern GFX cards).
This is similar to comparable platforms, like the SEGA Mega Drive and Nintendo SNES which both have somewhat of the same specs/power as the GBA.
On such platforms you need to calculate the 3D graphics yourself, paint it to a buffer in RAM and then "blit" that buffer to the 2D format which the console actually does understand.
There's of course several libraries for this, so you don't have to know 3D math to the core. However, for performance reasons, these libraries are likely replaced by game-specific routines, that are optimized specifically for your own game. Often this code is written in ARM assembly, which is the GBA's "fast" mode.
If you're interested in the source code for such stuff, check out the demo scene for GBA, by google-searching "gba homebrew".
You mention PS2 and Gamecube. Both of these have builtin 3D support - Like the PS1 and N64 before them.