As the given function is not periodic because of x^3 part and also by refering to the link https://www.desmos.com/calculator/cwpyyqjjmx we do not get any periodicity in the resultant graph.
For Even function F(-x) = F(x)
For Odd function F(-x) = -F(x)
Replacing x with -x in above function we get -(x^3) + x sin(x) which is neither even nor odd
The above function is Constant because it does involve constant term when we place the value of x then a constant will be there in the form of x^3 along with x sin(x)
Hence it will be Constant function
So option A is Correct.