Question

When used in a shorthand electron configuration, the noble gas core [He] represents 1s^2 2s^2 2p^6.

Answer 1

True; electron configuration for He is 1s^2, 2s^2, 2p^6

Answer 2

I think this is false.  If I remember correctly the noble gas core [He] represents 1s².  For example using the short hand notation for Boron you would do
[He] 2s²2p¹.

Hope this helps.  Let me know if you have any further questions or need any clarification.