Yes - there is an infinite number of such numbers. Just take the counting numbers (1,2,3,4, etc...) and put them to the power of 6 (i.e. multiply it by itself 6 times). The sequence of such numbers...
Any number to the 6th power will be both a squared number and a cubed number. The first 10 such numbers are: 1 64 729 4096 15625 46656 117649 262144 531441 1000000