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If you want to assume that v^3 + 2 vanishes, perhaps could you work in a quotient ring:

sage: I = R.ideal(v^3 + 2)
sage: I
Principal ideal (v^3 + 2) of Univariate Polynomial Ring in v over Finite Field of size 67
sage: S = R.quotient(I)
sage: S
Univariate Quotient Polynomial Ring in vbar over Finite Field of size 67 with modulus v^3 + 2

Then, you can send your poly in the quotient ring and compute its 67th power:

sage: P = S(poly)
sage: P
19*vbar^2 + 49*vbar + 8
sage: P^67
15*vbar^2 + 4*vbar + 8