So I don't know if you NEED to be using word storage and such, but really you were just over complicating it in doing so. All you needed was a simple loop which has a counter that increments by 2, checks if it is larger than the initial value, and then add that overall value to the result
.text
.globl main
initialize:
li $v0, 5 # Getting arg1 from user
syscall # System call
move $t0, $v0 # Store the input value in $t0
li $t1, 0 # Initializing the result register
li $t2, 0 # Initializing the addition/counter register
main:
loop:
add $t2, $t2, 2 # Increase the value to be added by 2 (next even value)
bge $t2, $t0, fin # Check if the increment is larger than or equal to the initial input, if so break to finish
add $t1, $t1, $t2 # Increment the result by adding the even value
j loop # jump bak to the top of the loop
fin:
li $v0,1 # let the system know an integer is going to be printed
move $a0, $t1 # Load the result into the $a0 register (the register that prints values)
syscall # System Call
li $v0, 10 # Let the system know the program is going to exit
syscall # System Call
So as you can see $t2 increments by 2 each time. After each increment it is compared to the input value. If the input ($t0) than $t2 then add the value of $t2 to the result ($t1). This way there is an increment counter which is also used to add the necessary even value to the result.
Edit:
Not sure if this is entirely what you meant but I just tossed in some loads and saves, using the s registers as those are the register that are supposed to be used when saving values.
.data
N: .word 0
Result: .word 0
.text
.globl main
initialize:
li $v0, 5 # Getting arg1 from user
syscall # System Call
la $s0, N # Load the address of N into $s0
sw $v0, 0($s0) # Store the input value in 0 index of N
li $t2, 0 # Initializing the addition/counter register
la $s1, Result # Load the address of Result into $s1
main:
sw $t2, 0($s1) # Setting the 0 index of Result to 0
loop:
add $t2, $t2, 2 # Increase the value to be added by 2 (next even value)
lw $t4, 0($s0) # Loading the input value into the $t4 register
bge $t2, $t4, fin # Check if the increment is larger than or equal to the initial input, if so break to finish
lw $t4, 0($s1) # Loading the current result into the $t4 register
add $t4, $t4, $t2 # Increment the result by adding the even value
sw $t4, 0($s1) # Saving the new current result into the $t4 register
j loop # jump bak to the top of the loop
fin:
li $v0,1 # let the system know an integer is going to be printed
lw $a0, 0($s1) # Load the result into the $a0 register (the register that prints values)
syscall # System Call
li $v0, 10 # Let the system know the program is going to exit
syscall # System Call