2³ doesn't just mean "2 cubed" — it means "2 multiplied by itself 3 times." On this page, first check what an exponent actually means, then see exactly why multiplying two exponents together adds their exponents.
An exponent is a shorthand for multiplying the same number several times. Instead of writing out 2×2×2 every time, writing 2³ is far simpler. Here, the repeated number 2 is called the base, and the number of times it's multiplied, 3, is called the exponent. Every time the exponent goes up by 1, the value doubles — growing far faster than anything addition could produce.
Exponents are great for describing quantities that grow extremely fast. The fact that 1KB of computer storage is exactly 2¹⁰ (=1024) bytes, and the way a bacteria colony doubles in size with every division, are both explained by exponents.
Ever wonder why multiplying two exponents with the same base just adds the exponents together? Switch between the tabs to work through it in order, from what an exponent means to the law of exponents.