Why can't I copy a 7 GB file to an external USB HD with 120 GB free?
Solution 1:
Maybe your External HDD is formatted as FAT? FAT-formatted drives can't see files larger than 4 GB, you'll have to reformat it as NTFS.
The maximum possible size for a file on a FAT32 volume is 4 GB minus 1 byte (232−1 bytes). Video applications, large databases, and some other software easily exceed this limit. Larger files require another formatting type such as NTFS.
FAT32 @ Wikipedia
Or you could split the zip file in two 3.5 GB parts.
Solution 2:
Most likely the drive has been formatted with FAT32 which has a maximum file size of 4GB. See the Wikipedia article on FAT32
Format the drive with NTFS and it should be good to go.