How to grow filesystem to use unallocated space in partition?

If gparted only has to extend the partition or filesystem into unused space (immediately following the partition), then it should be safe to let it extend the partition and/or fs.
If, however, it has to MOVE any partitions around to make space for resizing, you'll have to boot with a gparted Live CD
See the man page for resize2fs (which is the command-line tool gparted will use to grow an ext2, ext3, and ext4 filesystem) for more details about resizing those filesystems.

For ext2/3/4, growing a filesystem is generally not a problem and can safely be done while the fs is mounted.

Shrinking a filesystem, however, is more troublesome and should be done while the fs is unmounted. If it's the rootfs, that means booting to a rescue CD/USB/PXE etc.

BTW, both dd and cat are amongst the worst ways to copy a linux system to another hard disk. Use Clonezilla, that's what it's for.

sudo resize2fs /dev/sda6

will solve your problem.

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