Do we have an idea of what kind of wood the cross of Jesus was made out of?


No. The Bible doesn't say what type of wood was used and to speculate would be an exercise in futility.

"As I urged you when I went into Macedonia--remain in Ephesus that you may charge some that they teach no other doctrine, nor give heed to fables and endless genealogies, which cause disputes rather than godly edification which is in faith" (I Timothy 1:3-4).