From an information theory perspective, splitting the file isn't helping as much as you think, since each chunk is only 1/8th the size of the original file.
In your scheme, each chunk gives some information about the source file. In fact, it gives exactly 1/8th of the possible information
of the source file.
An area of cryptography called threshold secret sharing gives methods for dividing a "secret" into chunks distributed among n players such that any (t-1) or fewer pieces together give no information about the secret (they constitute entirely random information), but any t pieces together can reassemble the secret. In order for this to happen, the tth chunk had to contain as much information as the entire secret, so it had to be at least as large.
Secret sharing schemes are most often used for distributed signatures. A committee has a public key and shares the corresponding private key using threshold secret sharing, so that official statements can't be cryptographically signed unless more than half of the committee members agree to sign.
So in your case, encrypting the source, splitting, and then encrypting the pieces may help the case, but it's shaky ground from a theoretical standpoint.. You're probably no better off than just encrypting the source file without splitting it. If you really want to gain theoretical ground by splitting the file up, you should look into existing secret sharing schemes (wikipedia). With these, there's little need to encrypt the chunks, and (physically) separating the chunks has really helped.
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