An element has 8 protons and 8 neutrons in its nucleus and 8 electrons revolving around the nucleus. what is the atomic number and atomic mass of this element?

Atomic Number definition: The number of protons within the nucleus of x atom.

Atomic Mass definition: The number of protons and/+ neutrons within the nucleus of x atom. 

The given information states that the element has 8 protons and 8 neutrons in its nuclei with 8 electrons revolving around it. If the atomic number is 'the number of protons' and we have 8 given protons, our answer would be 8.  If the atomic mass is protons + neutrons and we have 8 protons and neutrons, our answer for atomic mass would inevitably be 16. 

Therefore

Atomic number: 8

Atomic mass: 16