Is it possible to power on a Linux machine automatically after powercut ? Without me having to press the power button ?
That's not something you can do using Linux, but rather what the BIOS is for.
In most BIOS versions there will be an option similar to "After power loss" with possible values like Power off and Reboot.
If the BIOS lacks such an option, you might possibly program your router to send a Wake-on-LAN packet on startup, but that depends on many factors.