Unresolved - Is continuity an irrelevant consequence

To show: for all real x,y
f(x^3+y^3)=(x+y)[ {f(x)^2} - {f(x)f(y)} + {f(y)^2} ]
implies that f(a*x)=a*f(x) for real a,x?

Partial work done when problem was posed at:

alt.math.undergrad
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subject: question
OP: sam hughes
date: 1-8-08

link:
http://groups.google.com/group/alt.math.undergrad/
browse_thread/thread/
6d629ac1dcb8932a/752ebeb0bf5a3798?lnk=st&q=#752ebeb0bf5a3798

When attacking, should one try to prove continuity, or is this a red
herring?
.