1. Stating the problem: Simplify the expression $$(4+3c^5)(4-3c^5)(4+3c^5)(4-3c^5)(4+3c^5)(4-3c^5)$$. 2. Notice the expression is of the form $$(a+b)(a-b)(a+b)(a-b)(a+b)(a-b)$$ which can be grouped as $$[(a+b)(a-b)]^3 = (a^2 - b^2)^3$$. 3. Identify $a=4$ and $b=3c^5$. 4. Use the difference of squares formula: $$(4+3c^5)(4-3c^5) = 4^2 - (3c^5)^2$$. 5. Calculate each square: $$4^2 = 16$$ and $$(3c^5)^2 = 9c^{10}$$. 6. Substitute back: $$16 - 9c^{10}$$. 7. Since the original expression is $$[(4+3c^5)(4-3c^5)]^3$$, we have: $$ (16 - 9c^{10})^3 $$. 8. The simplified form of the expression is $$\boxed{(16 - 9c^{10})^3}$$.