Arduino: 1.8.2 (Windows 10), Board: "Arduino/Genuino Mega or Mega 2560, ATmega2560 (Mega 2560)"
c:\program files (x86)\arduino\hardware\tools\avr\bin../lib/gcc/avr/4.9.2/../../../../avr/bin/ar.exe: unable to rename 'core\core.a'; reason: Permission denied
exit status 1
Error compiling for board Arduino/Genuino Mega or Mega 2560.
This report would have more information with
"Show verbose output during compilation"
option enabled in File -> Preferences.
This same error occurs with UNO R3 board. But both boards run on a my laptop.
Is this occuring for every sketch or only when Mega is selected?
A bunch of people have had IDE problems, including IDE crashes and bizarre compile errors, when they install a new version of the IDE. At least some of those problems seem to be caused by incompatible executables and preference files that the IDE saves outside the IDE installation directory. Perhaps that is what is causing your particular problem. In such cases it appears that the fix is to delete or rename the old "Arduino15" directory and re-install the new IDE.
On Mac OS X:
/Users/(username)/Library/Arduino15 (a.k.a. ~/Library/Arduino15)
(Note: The 'Library' folder is greyed out in Finder. The folder can't be opened with a double-click. To browse the contents of 'Library', ctrl-click on it and select "Open in New Tab" from the pop-up menu.)
On Windows delete or rename both:
Arduino IDE 1.6.5r5 and previous: C:\Users(username)\AppData\Roaming\Arduino15
Arduino IDE 1.6.6 and later: C:\Users(username)\AppData\Local\Arduino15
On Linux:
/home/(username)/.arduino15 (a.k.a. ~/.arduino15)
(Note: file/folder names starting with '.' are not normally shown in directory listings. Use 'ls -a' to get a directory listing that includes the hidden files.)