Can I change Intel (R) Pentium (R) CPU P6000 @ 1.87GHz, 1862 MHz to Core Core? If it can't be changed to what better CPU
To upgrade your processor, the new processor must be socket, chipset, and BIOS compatible. To determine what processors are BIOS compatible, you must ask the manufacturer of your system/motherboard. Then, you can select from those processors only. And, this is only possible if your existing processor is not soldered to the motherboard.
So, contact your system/motherboard manufacturer.
This is an Arrandale processor, which means it is a 1st generation Mobile Core family processor. Whether it can be upgraded is dependent upon (a) whether the processor is soldered to the laptop's motherboard (if it is, then no, it cannot be upgraded) and (b) which replacement (1st generation Mobile Core i3/i5/i7) processors are supported by the laptop's BIOS. As Al said, only the manufacturer of the laptop is going to be able to answer these questions for you.
My personal opinion: If it is even possible, it would be a waste of money to purchase an upgrade processor for this laptop. This is a 1st generation Core processor. The current generation is the 8th generation. The laptop is 7-8 years old. While it might run, Windows 10 is NOT supported on this laptop (by Microsoft or Intel). It's time to replace the whole thing with something much newer.