1sq + 3sq + 5sq +..............+(2n-1)sq = n/3(4nsq -1)

P(n) = 1² + 3² + 5² +... + (2n - 1)² = n/3(4n² - 1)
When n = 1,
LHS of P(1) = 1
RHS of P(1) = 1/3[4(1)² - 1]
                     = 1/3[4 - 1]
                    = 1/9
LHS ≠ RHS
So this is not possible.