When we looked at 4D algebras we saw that the algebras derived from CayleyDickson method produces the same algebras as the Clifford algebras, but now when we double up to 8D algebras, we see that the two classes of algebra start to diverge.
We can see that the tables for the algebras as different and further checking shows that the algebras are not isomorphic. The CayleyDickson have a conjugate and are therefore dividable but they are not associative. The Clifford algebras are associative but they may not have an inverse.
As we have seen on this page the type of each entry will be common for all these methods, it will be:

or equivalently in octonion notation: 

So to make the comparison clearer on the page we will only show the sign and colour code the entries so that the pattern will show:
8D CayleyDickson Algebras
DDD 
DDC  DCC  O = CCC  

i*j = j*i 




how these results were generated.
As the above link explains, the table was generated by a computer program from the (modified) CaleyDickson doubling process.
8D Clifford Algebras
That is, Clifford algebras based on 3 vector dimensions, I have tried the combinations of these dimensions squaring to positive and negative.
G 3,0,0 
G 2,1,0 
G 1,2,0 
G 0,3,0 


vectors anticommute 




how these results were generated.
As the above link explains, the table was generated by a computer program from the ordering of bases.
Even Subalgebras of 16D Clifford Algebras
That is, An even subalgebra of Clifford algebras based on 4 vector dimensions.
G+ 4,0,0 
G+ 3,1,0 
G+ 2,2,0 






G+ 0,4,0 
G+ 1,3,0 




Further Reading
Cayley Table for Geometric Algebra: