500 ws2812b LEDs in a 40cm sphere will be like a second sun. It will be uncomfortable to look at. To power it with a battery will require a car battery and a high-current 12V to 5V converter.
A few high-brightness LEDs at the centre of the sphere will be enough. And because all the LEDs will be the same colour, there is little point using ws2812 LEDs. 3 Arduino pwm outputs and 3 npn transistors can drive a dozen 5mm common-anode RGB leds.