"Securely erasing a hard drive requires at least three passes"

"Securely erasing a hard drive requires randomly mixing ones and zeros"

"Securely erasing a hard drive requires 35 passes if you want to really be safe"

From my research, none of these is true. The simple facts are:

1. To securely erase a mechanical (i.e. "magnetic" or "platter") hard drive, write one pass of zeroes (or ones) to the entire drive.
2. To securely erase an SSD, just delete all the data. Not format. Delete.

References

This article nicely summarizes the research.

You Only Need to Wipe a Disk Once to Securely Erase It